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Volumn 122, Issue 1-3, 2002, Pages 93-115

Algorithms for the fixed linear crossing number problem

Author keywords

Branch and bound; Crossing number; Heuristic; Linear layout; Neural network

Indexed keywords


EID: 84867936858     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(01)00314-6     Document Type: Article
Times cited : (26)

References (53)
  • 1
    • 0002555329 scopus 로고
    • De Bruijn and Kautz networks: A competitor for the hypercube?
    • F. Andre, J.P. Verjus, Elsevier Amsterdam
    • J.-C. Bermond, and C. Peyrat De Bruijn and Kautz networks: a competitor for the hypercube? F. Andre, J.P. Verjus, Hypercube and Distributed Computers 1989 Elsevier Amsterdam
    • (1989) Hypercube and Distributed Computers
    • Bermond, J.-C.1    Peyrat, C.2
  • 3
    • 0021412333 scopus 로고
    • A framework for solving VLSI graph layout problems
    • S.N. Bhatt, and F.T. Leighton A framework for solving VLSI graph layout problems J. Comput. Systems Sci. 28 1984 300 343
    • (1984) J. Comput. Systems Sci. , vol.28 , pp. 300-343
    • Bhatt, S.N.1    Leighton, F.T.2
  • 4
    • 0026835958 scopus 로고
    • Embedding graphs in books: A survey
    • T. Bilski Embedding graphs in books: a survey IEE Proc. E 139 2 1992 134 138
    • (1992) IEe Proc. e , vol.139 , Issue.2 , pp. 134-138
    • Bilski, T.1
  • 5
    • 84986495442 scopus 로고
    • Circulants and their connectivities
    • F. Boesch, and R. Tindell Circulants and their connectivities J. Graph Theory 8 1984 487 499
    • (1984) J. Graph Theory , vol.8 , pp. 487-499
    • Boesch, F.1    Tindell, R.2
  • 7
    • 0027632003 scopus 로고
    • A new variation on hypercubes with smaller diameter
    • F.B. Chedid, and R.B. Chedid A new variation on hypercubes with smaller diameter Inform. Proc. Lett. 46 1993 275 280
    • (1993) Inform. Proc. Lett. , vol.46 , pp. 275-280
    • Chedid, F.B.1    Chedid, R.B.2
  • 10
    • 17144403558 scopus 로고    scopus 로고
    • Topological properties of some interconnection network graphs
    • R. Cimikowski Topological properties of some interconnection network graphs Congr. Numer. 121 1996 19 32
    • (1996) Congr. Numer. , vol.121 , pp. 19-32
    • Cimikowski, R.1
  • 11
    • 0030108741 scopus 로고    scopus 로고
    • A neural network algorithm for a graph layout problem
    • R. Cimikowski, and P. Shope A neural network algorithm for a graph layout problem IEEE Trans. Neural Networks 7 2 1996 341 345
    • (1996) IEEE Trans. Neural Networks , vol.7 , Issue.2 , pp. 341-345
    • Cimikowski, R.1    Shope, P.2
  • 13
    • 56249110015 scopus 로고
    • An upper bound to the crossing number of the complete graph drawn on the pages of a book
    • E. Damiani, and O. D'Antonia An upper bound to the crossing number of the complete graph drawn on the pages of a book J. Combin. Inform. System Sci. 19 1-2 1994 75 84
    • (1994) J. Combin. Inform. System Sci. , vol.19 , Issue.12 , pp. 75-84
    • Damiani, E.1    D'Antonia, O.2
  • 17
    • 0004536469 scopus 로고
    • Heuristics for reducing crossings in 2-layered networks
    • P. Eades, and D. Kelly Heuristics for reducing crossings in 2-layered networks Ars Combin. 21-A 1986 89 98
    • (1986) Ars Combin. , vol.21 A , pp. 89-98
    • Eades, P.1    Kelly, D.2
  • 18
    • 0026928229 scopus 로고
    • The crossed cube architecture for parallel computation
    • K. Efe The crossed cube architecture for parallel computation IEEE Trans. Parallel & Distrib. Systems 3 5 1992 513 524
    • (1992) IEEE Trans. Parallel & Distrib. Systems , vol.3 , Issue.5 , pp. 513-524
    • Efe, K.1
  • 20
    • 4043051730 scopus 로고    scopus 로고
    • On the Eggleton and Guy conjectured upper bound for the crossing number of the n-cube
    • L. Faria, and C.M.H. de Figueiredo On the Eggleton and Guy conjectured upper bound for the crossing number of the n-cube Math. Slovaca 50 2000 271 287
    • (2000) Math. Slovaca , vol.50 , pp. 271-287
    • Faria, L.1    De Figueiredo, C.M.H.2
  • 24
    • 0011666198 scopus 로고
    • The toroidal crossing number of the complete graph
    • R.K. Guy, T. Jenkyns, and J. Schaer The toroidal crossing number of the complete graph J. Combin. Theory 4 1968 376 390
    • (1968) J. Combin. Theory , vol.4 , pp. 376-390
    • Guy, R.K.1    Jenkyns, T.2    Schaer, J.3
  • 25
    • 0038944461 scopus 로고
    • Toroidal graphs with arbitrarily high crossing numbers
    • F. Harary, P.C. Kainen, and A.J. Schwenk Toroidal graphs with arbitrarily high crossing numbers Nanta Math. 6 1973 58 67
    • (1973) Nanta Math. , vol.6 , pp. 58-67
    • Harary, F.1    Kainen, P.C.2    Schwenk, A.J.3
  • 26
    • 0141667564 scopus 로고    scopus 로고
    • Embedding de Bruijn, Kautz and shuffle-exchange networks in books
    • T. Hasunuma, and Y. Shibata Embedding de Bruijn, Kautz and shuffle-exchange networks in books Discrete Appl. Math. 78 1997 103 116
    • (1997) Discrete Appl. Math. , vol.78 , pp. 103-116
    • Hasunuma, T.1    Shibata, Y.2
  • 27
    • 0021835689 scopus 로고
    • Neural computation of decisions in optimization problems
    • J. Hopfield, and D. Tank Neural computation of decisions in optimization problems Biol. Cybernet. 52 1985 141 152
    • (1985) Biol. Cybernet. , vol.52 , pp. 141-152
    • Hopfield, J.1    Tank, D.2
  • 28
    • 0002468332 scopus 로고    scopus 로고
    • 2-layer straightline crossing minimization: Performance of exact and heuristic algorithms
    • M. Jünger, and P. Mutzel 2-layer straightline crossing minimization: performance of exact and heuristic algorithms J. Graph Algorithms Appl. 1 1 1997 1 25
    • (1997) J. Graph Algorithms Appl. , vol.1 , Issue.1 , pp. 1-25
    • Jünger, M.1    Mutzel, P.2
  • 29
    • 4043053127 scopus 로고
    • The book thickness of a graph, II
    • P.C. Kainen The book thickness of a graph, II Congr. Numer. 71 1990 127 132
    • (1990) Congr. Numer. , vol.71 , pp. 127-132
    • Kainen, P.C.1
  • 31
    • 0011677948 scopus 로고
    • Bounds for the crossing number of the n-cube
    • T. Madej Bounds for the crossing number of the n-cube J. Graph Theory 15 1991 81 97
    • (1991) J. Graph Theory , vol.15 , pp. 81-97
    • Madej, T.1
  • 32
    • 0346834702 scopus 로고
    • On the page number of graphs
    • S.M. Malitz On the page number of graphs J. Algorithms 17 1 1994 71 84
    • (1994) J. Algorithms , vol.17 , Issue.1 , pp. 71-84
    • Malitz, S.M.1
  • 34
    • 51249194645 scopus 로고
    • A logical calculus of ideas imminent in nervous activity
    • W.S. McCulloch, and W.H. Pitts A logical calculus of ideas imminent in nervous activity Bull. Math. Biophys. 5 1943 115 133
    • (1943) Bull. Math. Biophys. , vol.5 , pp. 115-133
    • McCulloch, W.S.1    Pitts, W.H.2
  • 35
    • 33645699608 scopus 로고
    • Permutation procedure for minimising the number of crossings in a network
    • T.A.J. Nicholson Permutation procedure for minimising the number of crossings in a network Proc. IEE 115 1 1968 21 26
    • (1968) Proc. IEE , vol.115 , Issue.1 , pp. 21-26
    • Nicholson, T.A.J.1
  • 36
    • 0019563297 scopus 로고
    • The cube-connected cycles: A versatile network for parallel computation
    • F.P. Preparata, and J. Vuillemin The cube-connected cycles: a versatile network for parallel computation Comm. ACM 24 5 1981 300 309
    • (1981) Comm. ACM , vol.24 , Issue.5 , pp. 300-309
    • Preparata, F.P.1    Vuillemin, J.2
  • 39
    • 0020834827 scopus 로고
    • The DIOGENES approach to testable fault-tolerant arrays of processors
    • A.L. Rosenberg The DIOGENES approach to testable fault-tolerant arrays of processors IEEE Trans. Comput. C-32 10 1983 902 910
    • (1983) IEEE Trans. Comput. , vol.32 C , Issue.10 , pp. 902-910
    • Rosenberg, A.L.1
  • 40
    • 0011033080 scopus 로고    scopus 로고
    • Crossing numbers: Bounds and applications
    • I. Barany, K. Boroczky, Bolyai Soc. Math. Studies Akademia Kiado Budapest
    • F. Shahrokhi, O. Skora, L.A. Székely, and I. Vrto Crossing numbers: bounds and applications I. Barany, K. Boroczky, Intuitive Geometry Bolyai Soc. Math. Studies Vol. 6 1997 Akademia Kiado Budapest 179 206
    • (1997) Intuitive Geometry , vol.6 , pp. 179-206
    • Shahrokhi, F.1    Skora, O.2    Székely, L.A.3    Vrto, I.4
  • 44
    • 1542711034 scopus 로고
    • On crossing numbers of hypercubes and cube-connected cycles
    • O. Skora, and I. Vrto On crossing numbers of hypercubes and cube-connected cycles BIT 33 1993 232 237
    • (1993) BIT , vol.33 , pp. 232-237
    • Skora, O.1    Vrto, I.2
  • 45
    • 0028481584 scopus 로고
    • On VLSI layouts of the star graph and related networks, integration
    • O. Skora, and I. Vrto On VLSI layouts of the star graph and related networks, integration The VLSI J. 17 1994 83 93
    • (1994) The VLSI J. , vol.17 , pp. 83-93
    • Skora, O.1    Vrto, I.2
  • 46
    • 0030478525 scopus 로고    scopus 로고
    • A parallel stochastic optimization algorithm for finding mappings of the rectilinear minimal crossing problem
    • J.T. Thorpe, and F.C. Harris A parallel stochastic optimization algorithm for finding mappings of the rectilinear minimal crossing problem Ars Combin. 43 1996 135 148
    • (1996) Ars Combin. , vol.43 , pp. 135-148
    • Thorpe, J.T.1    Harris, F.C.2
  • 47
    • 0037648004 scopus 로고
    • A near-optimum parallel planarization algorithm
    • Y. Takefuji, and K.-C. Lee A near-optimum parallel planarization algorithm Science 245 1989 1221 1223
    • (1989) Science , vol.245 , pp. 1221-1223
    • Takefuji, Y.1    Lee, K.-C.2
  • 49
    • 84976820924 scopus 로고
    • Sorting using networks of queues and stacks
    • R.E. Tarjan Sorting using networks of queues and stacks J. Assoc. Comput. Mach. 19 1972 341 346
    • (1972) J. Assoc. Comput. Mach. , vol.19 , pp. 341-346
    • Tarjan, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.