메뉴 건너뛰기




Volumn 34, Issue 3, 2002, Pages 313-356

A Survey of Graph Layout Problems

Author keywords

Approximation algorithms; Complexity; Embedding; Heuristics; Layout; Parameterized complexity; Random graphs

Indexed keywords

COMPUTATIONAL BIOLOGY; GRAPH LAYOUT; PARAMETERIZED COMPLEXITY;

EID: 0344704289     PISSN: 03600300     EISSN: None     Source Type: Journal    
DOI: 10.1145/568522.568523     Document Type: Review
Times cited : (526)

References (261)
  • 2
    • 0002283083 scopus 로고
    • Single machine job sequencing with precedence constraints
    • ADOLPHSON, D. 1977. Single machine job sequencing with precedence constraints. SIAM J. Comput. 6, 40-54.
    • (1977) SIAM J. Comput. , vol.6 , pp. 40-54
    • Adolphson, D.1
  • 3
    • 0000912718 scopus 로고
    • Optimal linear ordering
    • ADOLPHSON, D. AND HU, T. C. 1973. Optimal linear ordering. SIAM J. Appl. Mathem. 25, 3, 403-423.
    • (1973) SIAM J. Appl. Mathem. , vol.25 , Issue.3 , pp. 403-423
    • Adolphson, D.1    Hu, T.C.2
  • 4
    • 33750994100 scopus 로고
    • 1, isoperimetric inequalities for graphs and superconcentrators
    • 1, isoperimetric inequalities for graphs and superconcentrators. J. Combinatorial Theory. Series B 38, 73-88.
    • (1985) J. Combinatorial Theory. Series B , vol.38 , pp. 73-88
    • Alon, N.1    Milman, V.2
  • 6
    • 25744459628 scopus 로고    scopus 로고
    • Intervalizing colored graphs is NP-complete for caterpillars with hair length 2
    • Dept. de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya
    • ÀLVAREZ, C., DÍAZ, J., AND SERNA, M. 1998. Intervalizing colored graphs is NP-complete for caterpillars with hair length 2. Technical report LSI 98-9-R, Dept. de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya.
    • (1998) Technical Report , vol.LSI 98-9-R
    • Àlvarez, C.1    Díaz, J.2    Serna, M.3
  • 7
    • 0035962751 scopus 로고    scopus 로고
    • The hardness of intervalizing four colored caterpillars
    • ÀLVAREZ, C., DÍAZ, J., AND SERNA, M. 2001. The hardness of intervalizing four colored caterpillars. Discrete Mathematics 235, 19-27.
    • (2001) Discrete Mathematics , vol.235 , pp. 19-27
    • Àlvarez, C.1    Díaz, J.2    Serna, M.3
  • 8
    • 84855639180 scopus 로고    scopus 로고
    • The proper interval colored graph problem for caterpillar trees
    • Dept. de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya
    • ÀLVAREZ, C. AND SERNA, M. 1999. The proper interval colored graph problem for caterpillar trees. Technical report LSI 99-12-R, Dept. de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya.
    • (1999) Technical Report , vol.LSI 99-12-R
    • Àlvarez, C.1    Serna, M.2
  • 10
    • 0033077325 scopus 로고    scopus 로고
    • Polynomial time approximation schemes for dense instances of NP-hard problems
    • ARORA, S., KARGER, D., AND KARPINSKI, M. 1999. Polynomial time approximation schemes for dense instances of NP-hard problems. J. Comput. Syst. Sci. 58, 1, 193-210.
    • (1999) J. Comput. Syst. Sci. , vol.58 , Issue.1 , pp. 193-210
    • Arora, S.1    Karger, D.2    Karpinski, M.3
  • 13
    • 84855633382 scopus 로고    scopus 로고
    • The isoperimetric number and the bisection width of generalized cylinders
    • To appear
    • AZIZOǦLU, C. AND EǦECIOǦLU, Ö. 2002. The isoperimetric number and the bisection width of generalized cylinders. Discrete Mathematics. To appear.
    • (2002) Discrete Mathematics
    • Azizoǧlu, C.1    Eǧecioǧlu, Ö.2
  • 16
    • 0028419680 scopus 로고
    • A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems
    • BARNARD, S. T. AND SIMON, H. D. 1994. A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Concurrency: Practice and Experience 6, 101-107.
    • (1994) Concurrency: Practice and Experience , vol.6 , pp. 101-107
    • Barnard, S.T.1    Simon, H.D.2
  • 18
    • 0032665591 scopus 로고    scopus 로고
    • Greedy, prohibition, and reactive heuristics for graph partitioning
    • BATTITI, R. AND BERTOSSI, A. 1999. Greedy, prohibition, and reactive heuristics for graph partitioning. IEEE Trans. Comput. 48, 4, 361-385.
    • (1999) IEEE Trans. Comput. , vol.48 , Issue.4 , pp. 361-385
    • Battiti, R.1    Bertossi, A.2
  • 21
    • 0002067484 scopus 로고    scopus 로고
    • Path optimization for graph partitioning problems
    • BERRY, J. W. AND GOLDBERG, M. K. 1999. Path optimization for graph partitioning problems. Discrete Applied Mathematics 90, 27-50.
    • (1999) Discrete Applied Mathematics , vol.90 , pp. 27-50
    • Berry, J.W.1    Goldberg, M.K.2
  • 22
    • 0003386622 scopus 로고    scopus 로고
    • Edge isoperimetric problems on graphs (a survey)
    • L. Lovasz, A. Gyarfas, G. O. H. Katona, A. Recski, and L. Szekely, Eds. János Bolyai Math. Soc.
    • BEZRUKOV, S. L. 1999. Edge isoperimetric problems on graphs (a survey). In Graph Theory and Combinatorial Biology (Balatonlelle, 1996), L. Lovasz, A. Gyarfas, G. O. H. Katona, A. Recski, and L. Szekely, Eds. János Bolyai Math. Soc., 157-197.
    • (1999) Graph Theory and Combinatorial Biology (Balatonlelle, 1996) , pp. 157-197
    • Bezrukov, S.L.1
  • 24
    • 84958779018 scopus 로고    scopus 로고
    • New spectral lower bounds on the bisection width of graphs
    • U. Brandes and D. Wagner, Eds. Lecture Notes in Computer Science, Springer-Verlag
    • BEZRUKOV, S. L., ELSÄSSER, R., MONIEN, B., PREIS, R., AND TILLICH, J.-P. 2000b. New spectral lower bounds on the bisection width of graphs. In Graph-Theoretic Concepts in Computer Science, U. Brandes and D. Wagner, Eds. Lecture Notes in Computer Science, vol. 1928. Springer-Verlag, 23-34.
    • (2000) Graph-theoretic Concepts in Computer Science , vol.1928 , pp. 23-34
    • Bezrukov, S.L.1    Elsässer, R.2    Monien, B.3    Preis, R.4    Tillich, J.-P.5
  • 25
    • 0021412333 scopus 로고
    • A framework for solving VLSI graph layout problems
    • BHATT, S. N. AND LEIGHTON, F. T. 1984. A framework for solving VLSI graph layout problems. J. Comput. Syst. Sci. 28, 300-343.
    • (1984) J. Comput. Syst. Sci. , vol.28 , pp. 300-343
    • Bhatt, S.N.1    Leighton, F.T.2
  • 27
    • 26944485960 scopus 로고    scopus 로고
    • On approximation intractability of the bandwidth problem
    • Electronic Colloquium on Computational Complexity
    • BLACHE, G., KARPINSKI, M., AND WIRTGEN, J. 1998. On approximation intractability of the bandwidth problem. Technical report TR98-014, Electronic Colloquium on Computational Complexity.
    • (1998) Technical Report , vol.TR98-014
    • Blache, G.1    Karpinski, M.2    Wirtgen, J.3
  • 28
    • 0344791807 scopus 로고    scopus 로고
    • Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
    • BLUM, A., KONJEVOD, G., RAVI, R., AND VEMPALA, S. 2000. Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems. Theoretical Computer Science 235, 1, 25-42.
    • (2000) Theoretical Computer Science , vol.235 , Issue.1 , pp. 25-42
    • Blum, A.1    Konjevod, G.2    Ravi, R.3    Vempala, S.4
  • 30
    • 85037918238 scopus 로고
    • A tourist guide through treewidth
    • BODLAENDER, H. L. 1993. A tourist guide through treewidth. Acta Cybernetica 11, 1-2, 1-21.
    • (1993) Acta Cybernetica , vol.11 , Issue.1-2 , pp. 1-21
    • Bodlaender, H.L.1
  • 31
    • 0001294529 scopus 로고    scopus 로고
    • A linear-time algorithm for finding tree-decompositions of small treewidth
    • BODLAENDER, H. L. 1996. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25, 6, 1305-1317.
    • (1996) SIAM J. Comput. , vol.25 , Issue.6 , pp. 1305-1317
    • Bodlaender, H.L.1
  • 32
    • 0042542464 scopus 로고    scopus 로고
    • On intervalizing k-colored graphs for DNA physical mapping
    • BODLAENDER, H. L. AND DB FLUITER, B. 1996. On intervalizing k-colored graphs for DNA physical mapping. Discrete Applied Mathematics 71, 1-3, 55-77.
    • (1996) Discrete Applied Mathematics , vol.71 , Issue.1-3 , pp. 55-77
    • Bodlaender, H.L.1    De Fluiter, B.2
  • 33
    • 0008799320 scopus 로고
    • Approximating treewidth, pathwidth, and minimum elimination tree height
    • BODLAENDER, H. L., GILBERT, J. R., HAFSTEINSSON, H., AND KLOKS, T. 1995a. Approximating treewidth, pathwidth, and minimum elimination tree height. J. Algor. 18, 238-255.
    • (1995) J. Algor. , vol.18 , pp. 238-255
    • Bodlaender, H.L.1    Gilbert, J.R.2    Hafsteinsson, H.3    Kloks, T.4
  • 37
    • 0000748606 scopus 로고
    • Edge-isoperimetric inequalities in the grid
    • BOLLOBÁS, B. AND LEADER, I. 1991. Edge-isoperimetric inequalities in the grid. Combinatorica 4, 299-314.
    • (1991) Combinatorica , vol.4 , pp. 299-314
    • Bollobás, B.1    Leader, I.2
  • 41
    • 51249170866 scopus 로고
    • Graph bisection algorithms with good average case behavior
    • BUI, T., CHAUDHURI, S., LEIGHTON, T., AND SIPSER, M. 1987. Graph bisection algorithms with good average case behavior. Combinatorica 7, 171-191.
    • (1987) Combinatorica , vol.7 , pp. 171-191
    • Bui, T.1    Chaudhuri, S.2    Leighton, T.3    Sipser, M.4
  • 42
    • 0039709433 scopus 로고
    • Partitioning planar graphs
    • BUI, T. N. AND PECK, A. 1992. Partitioning planar graphs. SIAM J. Comput. 21, 2, 203-215.
    • (1992) SIAM J. Comput. , vol.21 , Issue.2 , pp. 203-215
    • Bui, T.N.1    Peck, A.2
  • 48
    • 0040340675 scopus 로고
    • Bandwidth of the composition of certain graph powers
    • CHINN, P. Z., LIN, Y. X., YUAN, J. J., AND WILLIAMS, K. 1995. Bandwidth of the composition of certain graph powers. Ars Combinatoria 39, 167-173.
    • (1995) Ars Combinatoria , vol.39 , pp. 167-173
    • Chinn, P.Z.1    Lin, Y.X.2    Yuan, J.J.3    Williams, K.4
  • 49
    • 0030497991 scopus 로고    scopus 로고
    • Parallel computing of physical maps - A comparative study in SIMD and MIMD parallelism
    • CHIRRAVURI, S., BHANDARKAR, S. M., AND ARNOLD, J. 1996. Parallel computing of physical maps - A comparative study in SIMD and MIMD parallelism. Journal of Computational Biology 3, 4, 503-528.
    • (1996) Journal of Computational Biology , vol.3 , Issue.4 , pp. 503-528
    • Chirravuri, S.1    Bhandarkar, S.M.2    Arnold, J.3
  • 50
    • 0037476529 scopus 로고
    • Academic Press, San Diego
    • CHUNG, F. R. K. 1988. Labelings of Graphs. Academic Press, San Diego, 151-168.
    • (1988) Labelings of Graphs , pp. 151-168
    • Chung, F.R.K.1
  • 53
    • 0040255299 scopus 로고
    • Optimal labelling of a product of two paths
    • CHVÁTALOVÁ, J. 1975. Optimal labelling of a product of two paths. Discrete Mathematics 11, 249-253.
    • (1975) Discrete Mathematics , vol.11 , pp. 249-253
    • Chvátalová, J.1
  • 54
    • 0011431888 scopus 로고
    • The bandwidth problem for graphs - A collection of recent results
    • Dept. of Computer Science, Southern Methodist University
    • CHVÁTALOVÁ, J., DEWDNEY, A., GIBBS, N., AND KoRFHAGE, R. 1975. The bandwidth problem for graphs - A collection of recent results. Technical report CS 75020, Dept. of Computer Science, Southern Methodist University.
    • (1975) Technical Report CS 75020
    • Chvátalová, J.1    Dewdney, A.2    Gibbs, N.3    Korfhage, R.4
  • 55
    • 0035580899 scopus 로고    scopus 로고
    • Algorithms for graph partitioning on the planted partition model
    • CONDON, A. AND KARP, R. M. 2001. Algorithms for graph partitioning on the planted partition model. Random Structures & Algorithms 18, 2, 116-140.
    • (2001) Random Structures & Algorithms , vol.18 , Issue.2 , pp. 116-140
    • Condon, A.1    Karp, R.M.2
  • 56
    • 0035947797 scopus 로고    scopus 로고
    • On weighted vs unweighted versions of combinatorial optimization problems
    • CRESCENZI, P., SILVESTRI, R., AND TREVISAN, L. 2001. On weighted vs unweighted versions of combinatorial optimization problems. Information and Computation 167, 1, 10-26.
    • (2001) Information and Computation , vol.167 , Issue.1 , pp. 10-26
    • Crescenzi, P.1    Silvestri, R.2    Trevisan, L.3
  • 60
    • 84855633938 scopus 로고
    • The δ-operator
    • L. Budach, Ed. Akademie-Verlag
    • DÍAZ, J. 1979. The δ-operator. In Fundamentals of Computation Theory, L. Budach, Ed. Akademie-Verlag, 105-111.
    • (1979) Fundamentals of Computation Theory , pp. 105-111
    • Díaz, J.1
  • 61
    • 85029651755 scopus 로고
    • Graph layout problems
    • I. M. Havel and V. Koubek, Eds. Lecture Notes in Computer Sciences, Springer-Verlag
    • DÍAZ, J. 1992. Graph layout problems. In Mathematical Foundations of Computer Science 1992, I. M. Havel and V. Koubek, Eds. Lecture Notes in Computer Sciences, vol. 629. Springer-Verlag, 14-23.
    • (1992) Mathematical Foundations of Computer Science 1992 , vol.629 , pp. 14-23
    • Díaz, J.1
  • 63
    • 0039463091 scopus 로고
    • The Minsumcut problem
    • F. Dehen, R. J. Sack, and N. Santoro, Eds. Lecture Notes in Computer Science, Springer-Verlag
    • DÍAZ, J., GIBBONS, A. M., PATERSON, M. S., AND TORÁN, J. 1991. The Minsumcut problem. In Algorithms and Data Structures, F. Dehen, R. J. Sack, and N. Santoro, Eds. Lecture Notes in Computer Science, vol. 519. Springer-Verlag, 65-79.
    • (1991) Algorithms and Data Structures , vol.519 , pp. 65-79
    • Díaz, J.1    Gibbons, A.M.2    Paterson, M.S.3    Torán, J.4
  • 64
    • 0034555999 scopus 로고    scopus 로고
    • Convergence theorems for some layout measures on random lattice and random geometric graphs
    • DÍAZ, J., PENROSE, M. D., PETIT, J., AND SERNA, M. 2000. Convergence theorems for some layout measures on random lattice and random geometric graphs. Combinatorics, Probability and Computing 9, 6, 489-511.
    • (2000) Combinatorics, Probability and Computing , vol.9 , Issue.6 , pp. 489-511
    • Díaz, J.1    Penrose, M.D.2    Petit, J.3    Serna, M.4
  • 65
    • 18044399942 scopus 로고    scopus 로고
    • Approximating layout problems on random geometric graphs
    • DÍAZ, J., PENROSE, M. D., PETIT, J., AND SERNA, M. 2001a. Approximating layout problems on random geometric graphs. J. Algorithms 39, 1, 78-116.
    • (2001) J. Algorithms , vol.39 , Issue.1 , pp. 78-116
    • Díaz, J.1    Penrose, M.D.2    Petit, J.3    Serna, M.4
  • 67
    • 0035962852 scopus 로고    scopus 로고
    • Approximating layout problems on random graphs
    • DÍAZ, J., PETIT, J., SERNA, M., AND TREVISAN, L. 2001c. Approximating layout problems on random graphs. Discrete Mathematics 235, 1-3, 245-253.
    • (2001) Discrete Mathematics , vol.235 , Issue.1-3 , pp. 245-253
    • Díaz, J.1    Petit, J.2    Serna, M.3    Trevisan, L.4
  • 69
    • 0040229169 scopus 로고
    • Communication throughput of interconnection networks
    • I. Privara, B. Rovan, and P. Ruzicka, Eds. Lecture Notes in Computer Science, Springer-Verlag
    • DIEKMANN, R., LÜLING, R., AND MONIEN, B. 1994. Communication throughput of interconnection networks. In Mathematical Foundations of Computer Science 1994, I. Privara, B. Rovan, and P. Ruzicka, Eds. Lecture Notes in Computer Science, vol. 841. Springer-Verlag, 72-86.
    • (1994) Mathematical Foundations of Computer Science 1994 , vol.841 , pp. 72-86
    • Diekmann, R.1    Lüling, R.2    Monien, B.3
  • 70
    • 0003114373 scopus 로고    scopus 로고
    • Combining helpful sets and parallel simulated annealing for the graph-partitioning problem
    • DIEKMANN, R., LÜLING, R., MONIEN, B., AND SPRÄNER, C. 1996. Combining helpful sets and parallel simulated annealing for the graph-partitioning problem. Parallel Algorithms and Applications 8, 61-84.
    • (1996) Parallel Algorithms and Applications , vol.8 , pp. 61-84
    • Diekmann, R.1    Lüling, R.2    Monien, B.3    Spräner, C.4
  • 71
    • 0039463054 scopus 로고
    • Using helpful sets to improve graph bisections
    • D. F. Hsu, A. L. Rosenberg, and D. Sotteau, Eds. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. AMS Press
    • DIEKMANN, R., MONIEN, B., AND PREIS, R. 1995. Using helpful sets to improve graph bisections. In Interconnection Networks and Mapping and Scheduling Parallel Computations, D. F. Hsu, A. L. Rosenberg, and D. Sotteau, Eds. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. AMS Press, 57-73.
    • (1995) Interconnection Networks and Mapping and Scheduling Parallel Computations , pp. 57-73
    • Diekmann, R.1    Monien, B.2    Preis, R.3
  • 72
    • 0000027962 scopus 로고
    • Edge separators for planar and outerplanar graphs with applications
    • DIKS, K., DJIDJEV, H., SÝROKA, O., AND VRŤO, I. 1993. Edge separators for planar and outerplanar graphs with applications. Journal of Algorithms 14, 258-279.
    • (1993) Journal of Algorithms , vol.14 , pp. 258-279
    • Diks, K.1    Djidjev, H.2    Sýroka, O.3    Vrťo, I.4
  • 73
    • 84987493196 scopus 로고
    • Some results on tree decomposition of graphs
    • DING, G. AND OPOROWSKI, B. 1995. Some results on tree decomposition of graphs. J. Graph Theory 20, 4, 481-499.
    • (1995) J. Graph Theory , vol.20 , Issue.4 , pp. 481-499
    • Ding, G.1    Oporowski, B.2
  • 75
    • 0029290085 scopus 로고
    • Fixed-parameter tractability and completeness II: On completeness for W
    • DOWNEY, R. G. AND FELLOWS, M. R. 1995. Fixed-parameter tractability and completeness II: On completeness for W[1], Theoretical Computer Science 141, 1-2, 109-131.
    • (1995) Theoretical Computer Science , vol.141 , Issue.1-2 , pp. 109-131
    • Downey, R.G.1    Fellows, M.R.2
  • 77
    • 84923106972 scopus 로고    scopus 로고
    • On Euclidean embeddings and bandwidth minimization
    • M. Goemans, K. Jansen, J. Rolim, and L. Trevisan, Eds. Lecture Notes in Computer Science, Springer-Verlag
    • DUNAGAN, J. AND VEMPALA, S. 2001. On Euclidean embeddings and bandwidth minimization. In Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques, M. Goemans, K. Jansen, J. Rolim, and L. Trevisan, Eds. Lecture Notes in Computer Science, vol. 2129. Springer-Verlag, 229-240.
    • (2001) Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques , vol.2129 , pp. 229-240
    • Dunagan, J.1    Vempala, S.2
  • 79
    • 0011092295 scopus 로고    scopus 로고
    • Graph partitioning - A survey
    • Technische Universitat Chemnitz
    • ELSNER, U. 1997. Graph partitioning - A survey. Technical Report 393, Technische Universitat Chemnitz.
    • (1997) Technical Report , vol.393
    • Elsner, U.1
  • 80
    • 0033340828 scopus 로고    scopus 로고
    • Fast approximate graphs algorithms
    • EVEN, G., NAOR, J., RAO, S., AND SCHIEBER, B. 1999. Fast approximate graphs algorithms. SIAM J. Comput. 28, 6, 2187-2214.
    • (1999) SIAM J. Comput. , vol.28 , Issue.6 , pp. 2187-2214
    • Even, G.1    Naor, J.2    Rao, S.3    Schieber, B.4
  • 81
    • 0001545727 scopus 로고    scopus 로고
    • Divide-and-conquer approximation algorithms via spreading metrics
    • EVEN, G., NAOR, J., RAO, S., AND SCHIEBER, B. 2000. Divide-and-conquer approximation algorithms via spreading metrics. J. ACM 47, 4, 585-616.
    • (2000) J. ACM , vol.47 , Issue.4 , pp. 585-616
    • Even, G.1    Naor, J.2    Rao, S.3    Schieber, B.4
  • 83
    • 0004086477 scopus 로고
    • NP-completeness of several arrangement problems
    • Dept. of Computer Science, Technion, Haifa
    • EVEN, S. AND SHILOACH, Y. 1975. NP-completeness of several arrangement problems. Technical Report TR-43, Dept. of Computer Science, Technion, Haifa.
    • (1975) Technical Report , vol.TR-43
    • Even, S.1    Shiloach, Y.2
  • 84
    • 0018311887 scopus 로고
    • A comparison of three resequencing algorithms for the reduction of matrix profile and wavefront
    • EVERSTINE, G. C. 1979. A comparison of three resequencing algorithms for the reduction of matrix profile and wavefront. Int. J. Num. Meth. Eng. 14, 837-853.
    • (1979) Int. J. Num. Meth. Eng. , vol.14 , pp. 837-853
    • Everstine, G.C.1
  • 85
    • 0034206224 scopus 로고    scopus 로고
    • Approximating the bandwidth via volume respecting embeddings
    • FEIGE, U. 2000. Approximating the bandwidth via volume respecting embeddings. J. Comput. Syst. Sci. 60, 3, 510-539.
    • (2000) J. Comput. Syst. Sci. , vol.60 , Issue.3 , pp. 510-539
    • Feige, U.1
  • 86
    • 0344359894 scopus 로고    scopus 로고
    • Improved performance guarantees for bandwidth minimization heuristics
    • Computer Science Dept., Weizmann Inst. Tech.
    • FEIGE, U. AND KHAUTHGAMER, R. 1998. Improved performance guarantees for bandwidth minimization heuristics (draft). Technical Report, Computer Science Dept., Weizmann Inst. Tech.
    • (1998) Technical Report
    • Feige, U.1    Khauthgamer, R.2
  • 87
    • 0036519752 scopus 로고    scopus 로고
    • A polylogarithmic approximation of the minimum bisection
    • To appear
    • FEIGE, U. AND KRAUTHGAMER, R. 2002. A polylogarithmic approximation of the minimum bisection. SIAM J. Comput., To appear.
    • (2002) SIAM J. Comput.
    • Feige, U.1    Krauthgamer, R.2
  • 89
    • 85010136218 scopus 로고
    • DNA physical mapping: Three ways difficult
    • T. Lengauer, Ed. Number 726 in Lecture Notes in Computer Science. Springer-Verlag
    • FELLOWS, M. R., HALLET, M. T., AND WAREHAM, W. T. 1993. DNA physical mapping: Three ways difficult. In Algorithms-ESA'93, T. Lengauer, Ed. Number 726 in Lecture Notes in Computer Science. Springer-Verlag, 157-168.
    • (1993) Algorithms-ESA'93 , pp. 157-168
    • Fellows, M.R.1    Hallet, M.T.2    Wareham, W.T.3
  • 90
    • 0345654468 scopus 로고
    • Layout permutation problems and well-partially-ordered sets
    • MIT Press, Cambridge, MA
    • FELLOWS, M. R. AND LANGSTON, M. A. 1988. Layout permutation problems and well-partially-ordered sets. In Advanced Research in VLSI. MIT Press, Cambridge, MA, 315-327.
    • (1988) Advanced Research in VLSI , pp. 315-327
    • Fellows, M.R.1    Langston, M.A.2
  • 91
    • 0002519830 scopus 로고
    • On well-partial-order theory and its application to combinatorial problems of VLSI design
    • FELLOWS, M. R. AND LANGSTON, M. A. 1992. On well-partial-order theory and its application to combinatorial problems of VLSI design. SIAM J. Discrete Mathem. 5, 1, 117-126.
    • (1992) SIAM J. Discrete Mathem. , vol.5 , Issue.1 , pp. 117-126
    • Fellows, M.R.1    Langston, M.A.2
  • 92
    • 0028713860 scopus 로고
    • On search, decision, and the efficiency of polynomial-time algorithms
    • FELLOWS, M. R. AND LANGSTON, M. A. 1994. On search, decision, and the efficiency of polynomial-time algorithms. J. Comput. Syst. Sci. 49, 3, 769-779.
    • (1994) J. Comput. Syst. Sci. , vol.49 , Issue.3 , pp. 769-779
    • Fellows, M.R.1    Langston, M.A.2
  • 93
    • 0042782992 scopus 로고    scopus 로고
    • Optimal linear arrangement of a rectangular grid
    • FISHBURN, P., TETALI, P., AND WINKLER, P. 2000. Optimal linear arrangement of a rectangular grid. Discrete Mathematics 213, 123-139.
    • (2000) Discrete Mathematics , vol.213 , pp. 123-139
    • Fishburn, P.1    Tetali, P.2    Winkler, P.3
  • 101
    • 0012658765 scopus 로고
    • Some NP-complete problems on graphs
    • John Hopkins University, Baltimore
    • GAVRIL, F. 1977. Some NP-complete problems on graphs. In 11th Conference on Information Sciences and Systems. John Hopkins University, Baltimore, 91-95.
    • (1977) 11th Conference on Information Sciences and Systems , pp. 91-95
    • Gavril, F.1
  • 102
    • 0016939622 scopus 로고
    • An algorithm for reducing the bandwidth and profile of a sparse matrix
    • GIBBS, N. E., POOLE, JR., W. G., AND STOCKMEYER, P. K. 1976. An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J. Num. Anal. 13, 2, 236-250.
    • (1976) SIAM J. Num. Anal. , vol.13 , Issue.2 , pp. 236-250
    • Gibbs, N.E.1    Poole Jr., W.G.2    Stockmeyer, P.K.3
  • 105
    • 0038256672 scopus 로고
    • An algorithm for minimal numeration of tree vertices
    • In Russian
    • GOLDBERG, M. K. AND KLIPKER, I. A. 1976. An algorithm for minimal numeration of tree vertices. Sakharth. SSR Mecn. Akad. Moambe 81, 3, 553-556. In Russian.
    • (1976) Sakharth. SSR Mecn. Akad. Moambe. , vol.81 , Issue.3 , pp. 553-556
    • Goldberg, M.K.1    Klipker, I.A.2
  • 107
    • 0344791802 scopus 로고    scopus 로고
    • The total vertex separation number of a graph
    • In Russian
    • GOLOVACH, P. A. 1997. The total vertex separation number of a graph. Diskretnaya Matematika 9, 4, 86-91. In Russian.
    • (1997) Diskretnaya Matematika , vol.9 , Issue.4 , pp. 86-91
    • Golovach, P.A.1
  • 108
    • 0345654466 scopus 로고    scopus 로고
    • The total vertex separation number and the profile of graphs
    • In Russian
    • GOLOVACH, P. A. AND FOMIN, F. V. 1998. The total vertex separation number and the profile of graphs. Diskretnaya Matematika 10, 1, 87-94. In Russian.
    • (1998) Diskretnaya Matematika , vol.10 , Issue.1 , pp. 87-94
    • Golovach, P.A.1    Fomin, F.V.2
  • 112
    • 0027694565 scopus 로고
    • Complexity and algorithms for reasoning about time: A graph theoretical approach
    • GOLUMBIC, M. C. AND SHAMIR, R. 1993. Complexity and algorithms for reasoning about time: A graph theoretical approach. J. ACM 40, 1108-1113.
    • (1993) J. ACM , vol.40 , pp. 1108-1113
    • Golumbic, M.C.1    Shamir, R.2
  • 116
    • 0344359893 scopus 로고    scopus 로고
    • Improved bandwidth approximation for trees and chordal graphs
    • GUPTA, A. 2001. Improved bandwidth approximation for trees and chordal graphs. J. Algor. 40, 1, 24-36.
    • (2001) J. Algor. , vol.40 , Issue.1 , pp. 24-36
    • Gupta, A.1
  • 117
    • 0037814216 scopus 로고
    • Improved dynamic programming algorithms for the bandwidth minimization and the mincut linear arrangement problem
    • GURARI, E. AND SUDBOROUGH, I. H. 1984. Improved dynamic programming algorithms for the bandwidth minimization and the mincut linear arrangement problem. J. Algor. 5, 531-546.
    • (1984) J. Algor. , vol.5 , pp. 531-546
    • Gurari, E.1    Sudborough, I.H.2
  • 118
    • 43949163804 scopus 로고
    • On the pathwidth of chordal graphs
    • GUSTEDT, J. 1993. On the pathwidth of chordal graphs. Discrete Applied Mathematics 45, 3, 233-248.
    • (1993) Discrete Applied Mathematics , vol.45 , Issue.3 , pp. 233-248
    • Gustedt, J.1
  • 119
    • 0036985979 scopus 로고    scopus 로고
    • Minimizing the profile of a symmetric matrix
    • HAGER, W. W. 2002. Minimizing the profile of a symmetric matrix. SIAM J. Sci. Comput. 23, 5, 1799-1816.
    • (2002) SIAM J. Sci. Comput. , vol.23 , Issue.5 , pp. 1799-1816
    • Hager, W.W.1
  • 120
    • 0024770523 scopus 로고
    • Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems
    • HANSEN, M. D. 1989. Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems. In 30th Annual Symposium on Foundations of Computer Science. 604-609.
    • (1989) 30th Annual Symposium on Foundations of Computer Science , pp. 604-609
    • Hansen, M.D.1
  • 121
    • 0031476959 scopus 로고    scopus 로고
    • Approximation algorithms for the bandwidth minimization problem for a large class of trees
    • HARALAMBIDES, J. AND MAKEDON, F. 1997. Approximation algorithms for the bandwidth minimization problem for a large class of trees. Theory of Computing Systems 30, 67-90.
    • (1997) Theory of Computing Systems , vol.30 , pp. 67-90
    • Haralambides, J.1    Makedon, F.2
  • 122
    • 0012361172 scopus 로고
    • Bandwidth minimization: An approximation algorithm for caterpillars
    • HARALAMBIDES, J., MAKEDON, F., AND MONIEN, B. 1991. Bandwidth minimization: an approximation algorithm for caterpillars. Mathematical Systems Theory 24, 169-177.
    • (1991) Mathematical Systems Theory , vol.24 , pp. 169-177
    • Haralambides, J.1    Makedon, F.2    Monien, B.3
  • 123
    • 0345222630 scopus 로고
    • Problem 16
    • M. Fiedler, Ed. Czechoslovak Academy Sciences
    • HARARY, P. 1967. Problem 16. In Graph Theory and Computing, M. Fiedler, Ed. Czechoslovak Academy Sciences, 161.
    • (1967) Graph Theory and Computing , pp. 161
    • Harary, P.1
  • 124
    • 0001394447 scopus 로고
    • Optimal assignments of numbers to vertices
    • HARPER, L. H. 1964. Optimal assignments of numbers to vertices. J. SIAM 12, 1, 131-135.
    • (1964) J. SIAM , vol.12 , Issue.1 , pp. 131-135
    • Harper, L.H.1
  • 125
    • 0001173412 scopus 로고
    • Optimal numberings and isoperimetric problems on graphs
    • HARPER, L. H. 1966. Optimal numberings and isoperimetric problems on graphs. J. Combinatorial Theory 1, 3, 385-393.
    • (1966) J. Combinatorial Theory , vol.1 , Issue.3 , pp. 385-393
    • Harper, L.H.1
  • 126
    • 0344359891 scopus 로고
    • Chassis layout and isoperimetric problems
    • Jet Propulsion Laboratory
    • HARPER, L. H. 1970. Chassis layout and isoperimetric problems. Technical Report SPS 37-66, vol II, Jet Propulsion Laboratory.
    • (1970) Technical Report SPS 37-66 , vol.2
    • Harper, L.H.1
  • 127
    • 0002368120 scopus 로고
    • Stabilization and the edge-sum problem
    • HARPER, L. H. 1977, Stabilization and the edge-sum problem. Ars Combinatoria 4, 225-270.
    • (1977) Ars Combinatoria , vol.4 , pp. 225-270
    • Harper, L.H.1
  • 129
    • 0011658780 scopus 로고
    • Comparing queues and stacks as mechanisms for laying out graphs
    • HEATH, L. S., LEIGHTON, F. T., AND ROSENBERG, A. L. 1992. Comparing queues and stacks as mechanisms for laying out graphs. SIAM J. Discrete Mathem. 5, 3, 398-412.
    • (1992) SIAM J. Discrete Mathem. , vol.5 , Issue.3 , pp. 398-412
    • Heath, L.S.1    Leighton, F.T.2    Rosenberg, A.L.3
  • 130
  • 131
    • 0032606848 scopus 로고    scopus 로고
    • Stack and queue layouts of directed acyclic graphs. II
    • HEATH, L. S. AND PEMMARAJU, S. V. 1999. Stack and queue layouts of directed acyclic graphs. II. SIAM J. Comput. 28, 5, 1588-1626.
    • (1999) SIAM J. Comput. , vol.28 , Issue.5 , pp. 1588-1626
    • Heath, L.S.1    Pemmaraju, S.V.2
  • 133
    • 0032667449 scopus 로고    scopus 로고
    • Stack and queue layouts of directed acyclic graphs. I
    • HEATH, L. S., PEMMARAJU, S. V., AND TRENK, A. N. 1999. Stack and queue layouts of directed acyclic graphs. I. SIAM J. Comput. 28, 4, 1510-1539.
    • (1999) SIAM J. Comput. , vol.28 , Issue.4 , pp. 1510-1539
    • Heath, L.S.1    Pemmaraju, S.V.2    Trenk, A.N.3
  • 134
    • 0026931094 scopus 로고
    • Laying out graphs using queues
    • HEATH, L. S. AND ROSENBERG, A. L. 1992, Laying out graphs using queues. SIAM J. Comput. 21, 5, 927-958.
    • (1992) SIAM J. Comput. , vol.21 , Issue.5 , pp. 927-958
    • Heath, L.S.1    Rosenberg, A.L.2
  • 136
    • 0040847675 scopus 로고
    • A spectral approach to bandwidth and separator problems in graphs
    • HELMBERG, C., RENDL, F., MOHAR, B., AND POLJAK, S. 1995. A spectral approach to bandwidth and separator problems in graphs. Linear and Multilinear Algebra 39, 1-2, 73-90.
    • (1995) Linear and Multilinear Algebra , vol.39 , Issue.1-2 , pp. 73-90
    • Helmberg, C.1    Rendl, F.2    Mohar, B.3    Poljak, S.4
  • 138
    • 0003573801 scopus 로고    scopus 로고
    • The Chaco user's guide: Version 2.0
    • HENDRICKSON, B. AND LELAND, R. 1997. The Chaco user's guide: version 2.0. Technical Report SAND94-2692, Sandia National Laboratories. ftp://ftp.cs.sandia.gov/pub/papers/bahendr/guide. ps.gz.
    • (1997) Technical Report , vol.SAND94-2692
    • Hendrickson, B.1    Leland, R.2
  • 140
    • 0000602164 scopus 로고
    • Optimum communication spanning trees
    • HU, T. C. 1974, Optimum communication spanning trees. SIAM J. Comput. 3, 188-195.
    • (1974) SIAM J. Comput. , vol.3 , pp. 188-195
    • Hu, T.C.1
  • 142
    • 0038928586 scopus 로고    scopus 로고
    • The Metropolis algorithm for graph bisection
    • JERRUM, M. AND SORKIN, G. 1998. The Metropolis algorithm for graph bisection. Discrete Applied Mathematics 82, 1-3, 155-175.
    • (1998) Discrete Applied Mathematics , vol.82 , Issue.1-3 , pp. 155-175
    • Jerrum, M.1    Sorkin, G.2
  • 143
    • 0024770085 scopus 로고
    • Optimization by simulated annealing: An experimental evaluation; part I, graph partitioning
    • JOHNSON, D. S., ARAGON, C. R., McGEOCH, L. A., AND SCHEVON, C. 1989. Optimization by simulated annealing: an experimental evaluation; part I, graph partitioning. Operations Research 37, 6, 865-892.
    • (1989) Operations Research , vol.37 , Issue.6 , pp. 865-892
    • Johnson, D.S.1    Aragon, C.R.2    Mcgeoch, L.A.3    Schevon, C.4
  • 144
    • 84986976912 scopus 로고
    • The complexity of the network design problem
    • JOHNSON, D. S., LENSTRA, J. K., AND KAN, A. H. G. R. 1978. The complexity of the network design problem. Networks 8, 4, 279-285.
    • (1978) Networks , vol.8 , Issue.4 , pp. 279-285
    • Johnson, D.S.1    Lenstra, J.K.2    Kan, A.H.G.R.3
  • 146
    • 38249011751 scopus 로고
    • Optimal linear labelings and eigenvalues of graphs
    • JUVAN, M. AND MOHAR, B. 1992. Optimal linear labelings and eigenvalues of graphs. Discrete Applied Mathematics 36, 2, 153-168.
    • (1992) Discrete Applied Mathematics , vol.36 , Issue.2 , pp. 153-168
    • Juvan, M.1    Mohar, B.2
  • 147
    • 21344440225 scopus 로고
    • Tabu search and genetic algorithms for the generalized graph partitioning problem
    • KADLUCZKA, P. AND WALA, K. 1995. Tabu search and genetic algorithms for the generalized graph partitioning problem. Control and Cybernetics 24, 4, 459-476.
    • (1995) Control and Cybernetics , vol.24 , Issue.4 , pp. 459-476
    • Kadluczka, P.1    Wala, K.2
  • 148
    • 0037668746 scopus 로고    scopus 로고
    • Pathwidth, bandwidth and completion problems to proper interval graphs with small cliques
    • KAPLAN, H. AND SHAMIR, R. 1996. Pathwidth, bandwidth and completion problems to proper interval graphs with small cliques. SIAM J. Comput. 25, 3, 540-561.
    • (1996) SIAM J. Comput. , vol.25 , Issue.3 , pp. 540-561
    • Kaplan, H.1    Shamir, R.2
  • 149
    • 0345222627 scopus 로고    scopus 로고
    • Bounded degree interval sandwich problems
    • KAPLAN, H. AND SHAMIR, R. 1999. Bounded degree interval sandwich problems. Algorithmica 24, 2, 96-104.
    • (1999) Algorithmica , vol.24 , Issue.2 , pp. 96-104
    • Kaplan, H.1    Shamir, R.2
  • 150
    • 0032606871 scopus 로고    scopus 로고
    • Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs
    • KAPLAN, H., SHAMIR, R., AND TARJAN, R. B. 1999. Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM J. Comput. 28, 5, 1906-1922.
    • (1999) SIAM J. Comput. , vol.28 , Issue.5 , pp. 1906-1922
    • Kaplan, H.1    Shamir, R.2    Tarjan, R.B.3
  • 151
    • 0033298274 scopus 로고    scopus 로고
    • A randomized fully polynomial time approximation scheme for the all-terminal network reliability problem
    • KARGER, D. R. 1999. A randomized fully polynomial time approximation scheme for the all-terminal network reliability problem. SIAM J. Comput. 29, 2, 492-514.
    • (1999) SIAM J. Comput. , vol.29 , Issue.2 , pp. 492-514
    • Karger, D.R.1
  • 153
    • 0242281033 scopus 로고    scopus 로고
    • An approximating algorithm for the bandwidth problem on dense graphs
    • Electronic Colloquium on Computational Complexity
    • KARPINSKI, M., WIRTGEN, J., AND ZELIKOVSKY, A. 1997. An approximating algorithm for the bandwidth problem on dense graphs. Technical Report TR 97-017, Electronic Colloquium on Computational Complexity.
    • (1997) Technical Report , vol.TR 97-017
    • Karpinski, M.1    Wirtgen, J.2    Zelikovsky, A.3
  • 155
    • 84972550099 scopus 로고
    • Incidence matrices, interval graphs, and seriation in archeology
    • KENDALL, D. G. 1969. Incidence matrices, interval graphs, and seriation in archeology. Pacific J. Mathem. 28, 565-570.
    • (1969) Pacific J. Mathem. , vol.28 , pp. 565-570
    • Kendall, D.G.1
  • 156
    • 84990479742 scopus 로고
    • An efficient heuristic procedure for partitioning graphs
    • KERNIGHAN, B. W. AND LIN, S. 1970. An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291-307.
    • (1970) Bell System Technical Journal , vol.49 , pp. 291-307
    • Kernighan, B.W.1    Lin, S.2
  • 157
    • 0014861466 scopus 로고
    • An automatic reordering schema for simultaneous equations derived from network system
    • KING, I. P. 1970. An automatic reordering schema for simultaneous equations derived from network system. Int. J. Numer. Meth. Eng. 2, 523-533.
    • (1970) Int. J. Numer. Meth. Eng. , vol.2 , pp. 523-533
    • King, I.P.1
  • 158
    • 0026897421 scopus 로고
    • The vertex separation number of a graph equals its path-width
    • KINNERSLEY, N. G. 1992. The vertex separation number of a graph equals its path-width. Information Processing Letters 42, 6, 345-350.
    • (1992) Information Processing Letters , vol.42 , Issue.6 , pp. 345-350
    • Kinnersley, N.G.1
  • 160
    • 0008801063 scopus 로고    scopus 로고
    • The relationship between the gossip complexity in vertex-disjoint paths mode and the vertex bisection width
    • KLASING, R. 1998. The relationship between the gossip complexity in vertex-disjoint paths mode and the vertex bisection width. Discrete Applied Mathematics 83, 229-246.
    • (1998) Discrete Applied Mathematics , vol.83 , pp. 229-246
    • Klasing, R.1
  • 161
    • 0011430418 scopus 로고
    • Computing the bandwidth of interval graphs
    • KLEITMAN, D. J. AND VOHRA, R. V. 1990. Computing the bandwidth of interval graphs. SIAM J. Discrete Mathem. 3, 3, 373-375.
    • (1990) SIAM J. Discrete Mathem. , vol.3 , Issue.3 , pp. 373-375
    • Kleitman, D.J.1    Vohra, R.V.2
  • 163
    • 0011423220 scopus 로고    scopus 로고
    • Approximating the bandwidth for asteroidal triple-free graphs
    • KLOKS, T., KRATSCH, D., AND MÜLLER, H. 1999. Approximating the bandwidth for asteroidal triple-free graphs. J. Algor. 32, 1, 41-57.
    • (1999) J. Algor. , vol.32 , Issue.1 , pp. 41-57
    • Kloks, T.1    Kratsch, D.2    Müller, H.3
  • 164
    • 0023397328 scopus 로고
    • Finding the minimum bandwidth of an interval graph
    • KRATSCH, D. 1987. Finding the minimum bandwidth of an interval graph. Information and Computation 74, 2, 140-158.
    • (1987) Information and Computation , vol.74 , Issue.2 , pp. 140-158
    • Kratsch, D.1
  • 165
    • 0000721299 scopus 로고    scopus 로고
    • Two improved algorithms for reducing the envelope and wavefront
    • KUMFERT, G. AND POTHEN, A. 1997. Two improved algorithms for reducing the envelope and wavefront. BIT 37, 3, 001-032.
    • (1997) BIT , vol.37 , Issue.3 , pp. 001-032
    • Kumfert, G.1    Pothen, A.2
  • 166
    • 0028378075 scopus 로고
    • The profile minimization problem in trees
    • KUO, D. AND CHANG, G. J. 1994. The profile minimization problem in trees. SIAM J. Comput. 23, 71-81.
    • (1994) SIAM J. Comput. , vol.23 , pp. 71-81
    • Kuo, D.1    Chang, G.J.2
  • 167
    • 0041404700 scopus 로고    scopus 로고
    • Ph.D. thesis, Dept. of Computer Science, Western Michigan Univ.
    • LAI, Y.-L. 1997. Bandwidth, edgesum and profile of graphs. Ph.D. thesis, Dept. of Computer Science, Western Michigan Univ.
    • (1997) Bandwidth, Edgesum and Profile of Graphs
    • Lai, Y.-L.1
  • 169
    • 0040934594 scopus 로고
    • Bandwidth for the sum of k graphs
    • LAI, Y.-L., LIU, J., AND WILLIAMS, K. 1994. Bandwidth for the sum of k graphs. Ars Combinatoria 37, 149-155.
    • (1994) Ars Combinatoria , vol.37 , pp. 149-155
    • Lai, Y.-L.1    Liu, J.2    Williams, K.3
  • 172
    • 0040094247 scopus 로고    scopus 로고
    • On bandwidth for the tensor product of paths and cycles
    • LAI, Y.-L. AND WILLIAMS, K. 1997. On bandwidth for the tensor product of paths and cycles. Discrete Applied Mathematics. 73, 2, 133-141.
    • (1997) Discrete Applied Mathematics , vol.73 , Issue.2 , pp. 133-141
    • Lai, Y.-L.1    Williams, K.2
  • 173
    • 0010786237 scopus 로고    scopus 로고
    • A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs
    • LAI, Y.-L. AND WILLIAMS, K. 1999. A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs. J. Graph Theory 31, 2, 75-94.
    • (1999) J. Graph Theory , vol.31 , Issue.2 , pp. 75-94
    • Lai, Y.-L.1    Williams, K.2
  • 176
    • 0000651166 scopus 로고    scopus 로고
    • Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
    • LEIGHTON, T. AND RAO, S. 1999. Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. J. ACM 46, 6, 787-832.
    • (1999) J. ACM , vol.46 , Issue.6 , pp. 787-832
    • Leighton, T.1    Rao, S.2
  • 178
    • 0028594881 scopus 로고
    • An empirical study of static load balancing algorithms
    • IEEE Computer Society Press
    • LELAND, R. AND HENDRICKSON, B. 1994. An empirical study of static load balancing algorithms. In Scalable High-Performance Computing Conference. IEEE Computer Society Press, 682-685.
    • (1994) Scalable High-performance Computing Conference , pp. 682-685
    • Leland, R.1    Hendrickson, B.2
  • 179
    • 0019689574 scopus 로고
    • Black-white pebbles and graph separation
    • LENGAUER, T. 1981. Black-white pebbles and graph separation. Acta Informatica 16, 465-475.
    • (1981) Acta Informatica , vol.16 , pp. 465-475
    • Lengauer, T.1
  • 180
    • 0004791043 scopus 로고
    • Upper and lower bounds on the complexity of the min-cut linear arrangements problem on trees
    • LENGAUER, T. 1982. Upper and lower bounds on the complexity of the min-cut linear arrangements problem on trees. SIAM J. Algeb. Discrete Meth. 3, 99-113.
    • (1982) SIAM J. Algeb. Discrete Meth. , vol.3 , pp. 99-113
    • Lengauer, T.1
  • 182
    • 0028400651 scopus 로고
    • Simulated annealing for profile and fill reduction of sparse matrices
    • LEWIS, R. 1994. Simulated annealing for profile and fill reduction of sparse matrices. Int. J. Num. Meth. Eng. 37, 6.
    • (1994) Int. J. Num. Meth. Eng. , vol.37 , pp. 6
    • Lewis, R.1
  • 186
    • 0039266344 scopus 로고
    • Assignments of numbers to vertices
    • LINDSEY, J. H. 1964. Assignments of numbers to vertices. American Mathematical Monthly 71, 508-516.
    • (1964) American Mathematical Monthly , vol.71 , pp. 508-516
    • Lindsey, J.H.1
  • 187
    • 0018457301 scopus 로고
    • A separator theorem for planar graphs
    • LIPTON, R. J. AND TARJAN, R. E. 1979. A separator theorem for planar graphs. SIAM J. Appl. Mathem. 36, 177-189.
    • (1979) SIAM J. Appl. Mathem. , vol.36 , pp. 177-189
    • Lipton, R.J.1    Tarjan, R.E.2
  • 189
    • 0041404698 scopus 로고
    • On bandwidth sum for the composition of paths and cycles
    • Dept. of Computer Science, Western Michigan Univ
    • LIU, J. 1992. On bandwidth sum for the composition of paths and cycles. Technical Report Rep/92-06, Dept. of Computer Science, Western Michigan Univ.
    • (1992) Technical Report Rep , vol.92 , Issue.6
    • Liu, J.1
  • 190
    • 0042407077 scopus 로고
    • On bandwidth and edgesum for the composition of two graphs
    • LIU, J. AND WILLIAMS, K. 1995. On bandwidth and edgesum for the composition of two graphs. Discrete Mathematics 143, 1-3, 159-166.
    • (1995) Discrete Mathematics , vol.143 , Issue.1-3 , pp. 159-166
    • Liu, J.1    Williams, K.2
  • 193
  • 197
    • 0037814215 scopus 로고
    • A simple linear-time algorithm for the recognition of bandwidth-2 biconnected garphs
    • MAKEDON, F., SHEINWALD, D., AND WOLFSTHAL, Y. 1993. A simple linear-time algorithm for the recognition of bandwidth-2 biconnected garphs. Information Processing Letters 46, 103-107.
    • (1993) Information Processing Letters , vol.46 , pp. 103-107
    • Makedon, F.1    Sheinwald, D.2    Wolfsthal, Y.3
  • 202
    • 0001478211 scopus 로고
    • Eigenvalues in combinatorial optimization
    • R. A. Brualdi, S. Friedland, and V. Klee, Eds. IMA Volumes in Mathematics and its Applications, Springer-Verlag
    • MOHAR, B. AND POLJAK, S. 1993. Eigenvalues in combinatorial optimization. In Combinatorial and Graph-Theoretical Problems in Linear Algebra, R. A. Brualdi, S. Friedland, and V. Klee, Eds. IMA Volumes in Mathematics and its Applications, vol. 50. Springer-Verlag, 107-151.
    • (1993) Combinatorial and Graph-theoretical Problems in Linear Algebra , vol.50 , pp. 107-151
    • Mohar, B.1    Poljak, S.2
  • 203
    • 0011517609 scopus 로고
    • The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
    • MONIEN, B. 1986. The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete. SIAM J. Algeb. Discrete Meth. 7, 4, 505-512.
    • (1986) SIAM J. Algeb. Discrete Meth. , vol.7 , Issue.4 , pp. 505-512
    • Monien, B.1
  • 204
    • 0024018788 scopus 로고
    • Min Cut is NP-complete for edge weighted trees
    • MONIEN, B. AND SUDBOHOUGH, I. H. 1988. Min Cut is NP-complete for edge weighted trees. Theoretical Computer Science 58, 1-3, 209-229.
    • (1988) Theoretical Computer Science , vol.58 , Issue.1-3 , pp. 209-229
    • Monien, B.1    Sudbohough, I.H.2
  • 205
    • 0000368053 scopus 로고
    • Embedding one interconnection network in another
    • G. Tinhofer, E. Mayr, H. Noltemeier, and M. M. Syslo, Eds. Computing Supplementa, Springer-Verlag
    • MONIEN, B. AND SUDBOROUGH, I. H. 1990. Embedding one interconnection network in another. In Computational Graph Theory, G. Tinhofer, E. Mayr, H. Noltemeier, and M. M. Syslo, Eds. Computing Supplementa, vol. 7. Springer-Verlag, 257-282.
    • (1990) Computational Graph Theory , vol.7 , pp. 257-282
    • Monien, B.1    Sudborough, I.H.2
  • 207
    • 0042643922 scopus 로고
    • Minimal numberings of a two-dimensional cylinder
    • In Russian
    • MURADYAN, D. O. 1982. Minimal numberings of a two-dimensional cylinder. Akademiya Nauk Armyanskoǐ SSR. Doklady 75, 3, 114-119. In Russian.
    • (1982) Akademiya Nauk Armyanskoǐ SSR. Doklady , vol.75 , Issue.3 , pp. 114-119
    • Muradyan, D.O.1
  • 208
    • 0043144853 scopus 로고
    • Some estimates for the length of an arbitrary graph
    • In Russian
    • MURADYAN, D. O. 1985. Some estimates for the length of an arbitrary graph. Mat. Voprosy Kibernet. Vychisl. Tekhn. 14, 79-86, 126. In Russian.
    • (1985) Mat. Voprosy Kibernet. Vychisl. Tekhn. , vol.14 , pp. 79-86
    • Muradyan, D.O.1
  • 209
    • 0043278334 scopus 로고
    • A polynomial algorithm for finding the bandwidth of interval graphs
    • In Russian
    • MURADYAN, D. O. 1986. A polynomial algorithm for finding the bandwidth of interval graphs. Akademiya Nauk Armyanskoǐ SSR. Doklady 82, 2, 64-66. In Russian.
    • (1986) Akademiya Nauk Armyanskoǐ SSR. Doklady , vol.82 , Issue.2 , pp. 64-66
    • Muradyan, D.O.1
  • 210
    • 0345222622 scopus 로고
    • Minimal numberings of vertices of a rectangular lattice
    • In Russian
    • MURADYAN, D. O. AND PILIPOSYAN, T. E. 1980. Minimal numberings of vertices of a rectangular lattice. Akad. Nauk. Armjan. SRR 1, 70, 21-27. In Russian.
    • (1980) Akad. Nauk. Armjan. SRR , vol.1 , Issue.70 , pp. 21-27
    • Muradyan, D.O.1    Piliposyan, T.E.2
  • 211
    • 0344359888 scopus 로고
    • The problem of finding the length and width of the complete p-partite graph
    • In Russian
    • MURADYAN, D. O. AND PILIPOSYAN, T. E. 1980. The problem of finding the length and width of the complete p-partite graph. Uchen. Zapiski Erevan. Gosunivers, 2, 18-26. In Russian.
    • (1980) Uchen. Zapiski Erevan. Gosunivers. , vol.2 , pp. 18-26
    • Muradyan, D.O.1    Piliposyan, T.E.2
  • 212
    • 84947725280 scopus 로고
    • A polyhedral approach to planar augmentation and related problems
    • P. Spirakis, Ed. Lecture Notes in Computer Science, Springer-Verlag
    • MUTZEL, P. 1995. A polyhedral approach to planar augmentation and related problems. In Algorithms - ESA95, P. Spirakis, Ed. Lecture Notes in Computer Science, vol. 979. Springer-Verlag, 497-507.
    • (1995) Algorithms - ESA95 , vol.979 , pp. 497-507
    • Mutzel, P.1
  • 213
    • 85028471462 scopus 로고
    • Linear layouts of generalized hypercubes
    • J. van Leeuwen, Ed. Lecture Notes in Computer Science, Springer-Verlag
    • NAKANO, K. 1994, Linear layouts of generalized hypercubes. In Graph-Th eoretic Concepts in Computer Science, J. van Leeuwen, Ed. Lecture Notes in Computer Science, vol. 790. Springer-Verlag, 364-375.
    • (1994) Graph-theoretic Concepts in Computer Science , vol.790 , pp. 364-375
    • Nakano, K.1
  • 215
    • 0016881473 scopus 로고
    • The NP-completeness of the bandwidth minimization problem
    • PAPADIMITRIOU, C. 1976. The NP-completeness of the bandwidth minimization problem. Computing 16, 263-270.
    • (1976) Computing , vol.16 , pp. 263-270
    • Papadimitriou, C.1
  • 217
    • 0004699056 scopus 로고
    • Single linkage clustering and continuum percolation
    • PENROSE, M. 1995. Single linkage clustering and continuum percolation. J. Multivariate Anal. 53, 94-109.
    • (1995) J. Multivariate Anal. , vol.53 , pp. 94-109
    • Penrose, M.1
  • 218
    • 0034378089 scopus 로고    scopus 로고
    • Vertex ordering and partitioning problems for random spatial graphs
    • PENROSE, M. 2000. Vertex ordering and partitioning problems for random spatial graphs. The Annals of Applied Probability 10, 517-538.
    • (2000) The Annals of Applied Probability , vol.10 , pp. 517-538
    • Penrose, M.1
  • 219
    • 0344791796 scopus 로고    scopus 로고
    • Approximation heuristics and benchmarkings for the MINLA problem
    • R. Battiti and A. Bertossi, Eds.
    • PETIT, J. 1998. Approximation heuristics and benchmarkings for the MINLA problem. In Alex '98 - Building Bridges Between Theory and Applications, R. Battiti and A. Bertossi, Eds. 112-128.
    • (1998) Alex '98 - Building Bridges between Theory and Applications , pp. 112-128
    • Petit, J.1
  • 220
    • 25744463090 scopus 로고    scopus 로고
    • Combining spectral sequencing and parallel simulated annealing for the minLA problem
    • Departament de Llenguatges i Sistemes Informatics, Universitat Politècnica de Catalunya
    • PETIT, J. 2000. Combining spectral sequencing and parallel simulated annealing for the minLA problem. Technical Report LSI-01-13-R, Departament de Llenguatges i Sistemes Informatics, Universitat Politècnica de Catalunya.
    • (2000) Technical Report , vol.LSI-01-13-R
    • Petit, J.1
  • 221
    • 0013173275 scopus 로고    scopus 로고
    • Experiments for the MINLA problem
    • Departament de Llenguatges i Sistemes Informatics, Universitat Politècnica de Catalunya
    • PETIT, J. 2001a. Experiments for the MINLA problem. Technical Report LSI-R01-7-R, Departament de Llenguatges i Sistemes Informatics, Universitat Politècnica de Catalunya.
    • (2001) Technical Report , vol.LSI-R-7-R
    • Petit, J.1
  • 222
    • 0344359889 scopus 로고    scopus 로고
    • Ph.D. thesis, Universitat Politècnica de Catalunya
    • PETIT, J. 2001b. Layout problems. Ph.D. thesis, Universitat Politècnica de Catalunya.
    • (2001) Layout Problems
    • Petit, J.1
  • 223
    • 0003479963 scopus 로고    scopus 로고
    • The Party partitioning library user guide
    • Universität Paderborn
    • PREIS, R. AND DIEKMANN, R. 1996. The Party partitioning library user guide. Technical Report TR-RSFB-96-024, Universität Paderborn.
    • (1996) Technical Report , vol.TR-RSFB-96-024
    • Preis, R.1    Diekmann, R.2
  • 227
    • 0010057702 scopus 로고
    • Ordering problems approximated: Single-processor scheduling and interval graph completition
    • J. Leach, B. Monien, and M. Rodriguez, Eds. Lecture Notes in Computer Science, Springer-Verlag
    • RAVI, R., AGRAWAL, A., AND KLEIN, P. 1991. Ordering problems approximated: single-processor scheduling and interval graph completition. In Automata, Languages and Programming, J. Leach, B. Monien, and M. Rodriguez, Eds. Lecture Notes in Computer Science, vol. 510. Springer-Verlag, 751-762.
    • (1991) Automata, Languages and Programming , vol.510 , pp. 751-762
    • Ravi, R.1    Agrawal, A.2    Klein, P.3
  • 228
    • 0001814458 scopus 로고
    • Graph minors - A survey
    • Cambridge University Press
    • ROBERTSON, N. AND SEYMOUR, P. D. 1985. Graph minors - a survey. In Surveys in Combinatorics. Cambridge University Press, 153-171.
    • (1985) Surveys in Combinatorics , pp. 153-171
    • Robertson, N.1    Seymour, P.D.2
  • 229
    • 84948968922 scopus 로고
    • Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes
    • Lecture Notes in Computer Science, Springer
    • ROLIM, J., SÝKORA, O., AND VRŤO, I. 1995. Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes. In Graph Theoretic Concepts in Computer Science. Lecture Notes in Computer Science, vol. 1017. Springer, 252-264.
    • (1995) Graph Theoretic Concepts in Computer Science , vol.1017 , pp. 252-264
    • Rolim, J.1    Sýkora, O.2    Vrťo, I.3
  • 232
    • 0038490433 scopus 로고
    • Dynamic-programming algorithms for recognizing small-bandwidth graphs in polynomial time
    • SAXE, J. B. 1980. Dynamic-programming algorithms for recognizing small-bandwidth graphs in polynomial time. SIAM J. Algeb. Discrete Meth. 1, 4, 363-369.
    • (1980) SIAM J. Algeb. Discrete Meth. , vol.1 , Issue.4 , pp. 363-369
    • Saxe, J.B.1
  • 233
    • 34249756824 scopus 로고
    • Packing directed circuits fractionally
    • SEYMOUR, P. D. 1995. Packing directed circuits fractionally. Combinatorica 15, 2, 281-288.
    • (1995) Combinatorica , vol.15 , Issue.2 , pp. 281-288
    • Seymour, P.D.1
  • 234
    • 0038521887 scopus 로고
    • Call routing and the ratcatcher
    • SEYMOUR, P. D. AND THOMAS, R. 1994. Call routing and the ratcatcher. Combinatorica 14, 2, 217-241.
    • (1994) Combinatorica , vol.14 , Issue.2 , pp. 217-241
    • Seymour, P.D.1    Thomas, R.2
  • 236
    • 0035705976 scopus 로고    scopus 로고
    • On bipartite drawings and the linear arrangement problem
    • SHAHROKHI, P., SÝKORA, O., SZÉKELY, L. A., AND VRŤO, I. 2001. On bipartite drawings and the linear arrangement problem. SIAM J. Comput. 30, 6, 1773-1789.
    • (2001) SIAM J. Comput. , vol.30 , Issue.6 , pp. 1773-1789
    • Shahrokhi, P.1    Sýkora, O.2    Székely, L.A.3    Vrťo, I.4
  • 237
    • 0002107165 scopus 로고
    • A minimum linear arrangement algorithm for undirected trees
    • SHILOACH, Y. 1979. A minimum linear arrangement algorithm for undirected trees. SIAM J. Comput. 8, 1, 15-32.
    • (1979) SIAM J. Comput. , vol.8 , Issue.1 , pp. 15-32
    • Shiloach, Y.1
  • 238
    • 0041905824 scopus 로고
    • Computational complexity of layout problems
    • T. Ohtsuki, Ed. Advances in CAD for VLSI, North-Holland, Amsterdam
    • SHING, M. T. AND HU, T. C. 1986. Computational complexity of layout problems. In Layout Design and Verification, T. Ohtsuki, Ed. Advances in CAD for VLSI, vol. 4. North-Holland, Amsterdam, 267-294.
    • (1986) Layout Design and Verification , vol.4 , pp. 267-294
    • Shing, M.T.1    Hu, T.C.2
  • 239
    • 0031215997 scopus 로고    scopus 로고
    • How good is recursive bisection?
    • SIMON, H. D. AND TENG, S.-H. 1997. How good is recursive bisection? SIAM J. Sci. Comput. 18, 5, 1436-1445.
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.5 , pp. 1436-1445
    • Simon, H.D.1    Teng, S.-H.2
  • 240
    • 35649022756 scopus 로고    scopus 로고
    • Computing optimal linear layouts of trees in linear time
    • M. Paterson, Ed. Lecture Notes in Computer Science, Springer-Verlag
    • SKODINIS, K. 2000. Computing optimal linear layouts of trees in linear time. In Algorithms - ESA 2000, M. Paterson, Ed. Lecture Notes in Computer Science, vol. 1879. Springer-Verlag, 403-414.
    • (2000) Algorithms - ESA 2000 , vol.1879 , pp. 403-414
    • Skodinis, K.1
  • 243
    • 0011464935 scopus 로고
    • An O(n log n) algorithm for bandwidth of interval graphs
    • SPRAGUE, A. P. 1994. An O(n log n) algorithm for bandwidth of interval graphs. SIAM J. Discrete Mathem. 7, 2, 213-220.
    • (1994) SIAM J. Discrete Mathem. , vol.7 , Issue.2 , pp. 213-220
    • Sprague, A.P.1
  • 244
    • 0042359012 scopus 로고    scopus 로고
    • Bisection width of transposition graphs
    • STACHO, L. AND VRŤO, I. 1998. Bisection width of transposition graphs. Discrete Applied Mathematics 84, 1-3, 221-235.
    • (1998) Discrete Applied Mathematics , vol.84 , Issue.1-3 , pp. 221-235
    • Stacho, L.1    Vrťo, I.2
  • 245
    • 0027589605 scopus 로고
    • Edge separators for graphs of bounded genus with applications
    • SÝKORA, O. AND VRŤO, I. 1993. Edge separators for graphs of bounded genus with applications. Theoretical Computer Science 112, 419-429.
    • (1993) Theoretical Computer Science , vol.112 , pp. 419-429
    • Sýkora, O.1    Vrťo, I.2
  • 247
    • 84949808487 scopus 로고    scopus 로고
    • Constructive linear time algorithms for small cutwidth and carving-width
    • D. T. Lee and S.-H. Teng, Eds. Lecture Notes in Computer Science, Springer-Verlag
    • THILIKOS, D. M., SERNA, M. J., AND BODLAENDER, H. L. 2000. Constructive linear time algorithms for small cutwidth and carving-width. In ISAAC 2000 Algorithms and Computation, D. T. Lee and S.-H. Teng, Eds. Lecture Notes in Computer Science, vol. 1969. Springer-Verlag, 192-203.
    • (2000) ISAAC 2000 Algorithms and Computation , vol.1969 , pp. 192-203
    • Thilikos, D.M.1    Serna, M.J.2    Bodlaender, H.L.3
  • 248
    • 84943243932 scopus 로고    scopus 로고
    • A polynomial time algorithm for the cutwidth of bounded degree graphs with small treewidth
    • F. Meyer auf der Heide, Ed. Lecture Notes in Computer Science, Springer-Verlag
    • THILIKOS, D. M., SERNA, M. J., AND BODLAENDER, H. L. 2001. A polynomial time algorithm for the cutwidth of bounded degree graphs with small treewidth. In Algorithms, ESA 2001, F. Meyer auf der Heide, Ed. Lecture Notes in Computer Science, vol. 2161. Springer-Verlag, 380-390.
    • (2001) Algorithms, ESA 2001 , vol.2161 , pp. 380-390
    • Thilikos, D.M.1    Serna, M.J.2    Bodlaender, H.L.3
  • 250
    • 0022714383 scopus 로고
    • On the probable performance of heuristics for bandwidth minimization
    • TURNER, J. S. 1986. On the probable performance of heuristics for bandwidth minimization. SIAM J. Comput. 15, 2, 561-580.
    • (1986) SIAM J. Comput. , vol.15 , Issue.2 , pp. 561-580
    • Turner, J.S.1
  • 253
    • 17844377587 scopus 로고    scopus 로고
    • Cutwidth of the r-dimensional mesh of d-ary trees
    • VRŤO, I. 2000. Cutwidth of the r-dimensional mesh of d-ary trees. RAIRO Informatique Théorique et Applications 34, 6, 515-519.
    • (2000) RAIRO Informatique Théorique et Applications , vol.34 , Issue.6 , pp. 515-519
    • Vrťo, I.1
  • 258
    • 0033293966 scopus 로고    scopus 로고
    • A polynomial time approximation scheme for minimum routing cost spanning trees
    • WU, B. Y., LANCIA, G., BAFNA, V., CHAO, K.-M., RAVI, R., AND TANG, C. Y. 1999. A polynomial time approximation scheme for minimum routing cost spanning trees. SIAM J. Comput. 29, 3, 761-778.
    • (1999) SIAM J. Comput. , vol.29 , Issue.3 , pp. 761-778
    • Wu, B.Y.1    Lancia, G.2    Bafna, V.3    Chao, K.-M.4    Ravi, R.5    Tang, C.Y.6
  • 259
    • 0022146832 scopus 로고
    • A polynomial algorithm for the min-cut linear arrangement of trees
    • YANNAKAKIS, M. 1985. A polynomial algorithm for the min-cut linear arrangement of trees. J. ACM 32, 4, 950-988.
    • (1985) J. ACM , vol.32 , Issue.4 , pp. 950-988
    • Yannakakis, M.1
  • 260
    • 0344791793 scopus 로고    scopus 로고
    • NP-completeness of the profile problem and the fill-in problem on cobipartite graphs
    • YUAN, J., LIN, Y., LIU, Y., AND WANG, S. 1998. NP-completeness of the profile problem and the fill-in problem on cobipartite graphs. J. Mathem. Study 31, 3, 239-243.
    • (1998) J. Mathem. Study , vol.31 , Issue.3 , pp. 239-243
    • Yuan, J.1    Lin, Y.2    Liu, Y.3    Wang, S.4
  • 261
    • 0042786513 scopus 로고    scopus 로고
    • Harper-type lower bounds and the bandwidths of the compositions of graphs
    • ZHOU, S. AND YUAN, J. 1998. Harper-type lower bounds and the bandwidths of the compositions of graphs. Discrete Mathematics 181, 1-3, 255-266.
    • (1998) Discrete Mathematics , vol.181 , Issue.1-3 , pp. 255-266
    • Zhou, S.1    Yuan, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.