메뉴 건너뛰기




Volumn 48, Issue 2, 2001, Pages 206-242

Convex quadratic and semidefinite programming relaxations in scheduling

Author keywords

Approximation algorithms; Convex optimization; Performance guarantee; Randomized algorithms; Scheduling theory; Unrelated machines; Worst case ratio

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; LINEAR PROGRAMMING; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

EID: 0000093702     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/375827.375840     Document Type: Article
Times cited : (139)

References (57)
  • 4
    • 84927134775 scopus 로고    scopus 로고
    • On dependent randomized rounding algorithms
    • W. H. Cunningham, S. T. McCormick, and M. Queyranne, Eds., Lecture Notes in Computer Science . Springer-Verlag, Berlin, Germany
    • BERTSIMAS, D., TEO, C., AND VOHRA, R. 1996. On dependent randomized rounding algorithms. In Integer Programming and Combinatorial Optimization, W. H. Cunningham, S. T. McCormick, and M. Queyranne, Eds., Lecture Notes in Computer Science, vol. 1084. Springer-Verlag, Berlin, Germany.
    • (1996) Integer Programming and Combinatorial Optimization , vol.1084
    • Bertsimas, D.1    Teo, C.2    Vohra, R.3
  • 5
    • 84947720721 scopus 로고    scopus 로고
    • Improved scheduling algorithms for minsum criteria
    • F. Meyer auf der Heide and B. Monien, Eds. Lecture Notes in Computer Science . Springer-Verlag, Berlin, Germany
    • CHAKRABARTI, S., PHILLIPS, C., SCHULZ, A. S., SHMOYS, D. B., STEIN, C., AND WEIN, J. 1996. Improved scheduling algorithms for minsum criteria. In Automata, Languages and Programming. F. Meyer auf der Heide and B. Monien, Eds. Lecture Notes in Computer Science, vol. 1099. Springer-Verlag, Berlin, Germany.
    • (1996) Automata, Languages and Programming , vol.1099
    • Chakrabarti, S.1    Phillips, C.2    Schulz, A.S.3    Shmoys, D.B.4    Stein, C.5    Wein, J.6
  • 6
    • 0003593943 scopus 로고    scopus 로고
    • A geometric approach to betweenness
    • CHOR, B., AND SUDAN, M. 1998. A geometric approach to betweenness. SIAM J. Disc. Math. 11, 511-523.
    • (1998) SIAM J. Disc. Math. , vol.11 , pp. 511-523
    • Chor, B.1    Sudan, M.2
  • 7
    • 0242599114 scopus 로고    scopus 로고
    • A min-sum 3/2-approximation algorithm for scheduling unrelated parallel machines
    • CHUDAK, F. A. 1999. A min-sum 3/2-approximation algorithm for scheduling unrelated parallel machines. J. Sched. 2, 73-77.
    • (1999) J. Sched , vol.2 , pp. 73-77
    • Chudak, F.A.1
  • 8
    • 0000869985 scopus 로고    scopus 로고
    • Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speeds
    • CHUDAK, F. A., AND SHMOYS, D. B. 1999. Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speeds. J. Algor. 30, 323-343.
    • (1999) J. Algor. , vol.30 , pp. 323-343
    • Chudak, F.A.1    Shmoys, D.B.2
  • 9
    • 0004454684 scopus 로고
    • Polynomially bounded ellipsoid algorithms for convex quadratic programming
    • O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Eds. Academic Press, Orlando, Fla.
    • CHUNG, S. J., AND MURTY, K. G. 1981. Polynomially bounded ellipsoid algorithms for convex quadratic programming. In Nonlinear Programming, vol. 4, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Eds. Academic Press, Orlando, Fla., pp. 439-485.
    • (1981) Nonlinear Programming , vol.4 , pp. 439-485
    • Chung, S.J.1    Murty, K.G.2
  • 11
    • 0001559895 scopus 로고
    • Formulating the single machine sequencing problem with release dates as a mixed integer program
    • DYER, M. E., AND WOLSEY, L. A. 1990. Formulating the single machine sequencing problem with release dates as a mixed integer program. Disc. Appl. Math. 26, 255-270.
    • (1990) Disc. Appl. Math. , vol.26 , pp. 255-270
    • Dyer, M.E.1    Wolsey, L.A.2
  • 12
    • 84896765020 scopus 로고    scopus 로고
    • Techniques for scheduling with rejection
    • G. Bilardi, G. F. Italiano, A. Pietracaprina, and G. Pucci, Eds. Lecture Notes in Computer Science . Springer, Berlin, Germany
    • ENGELS, D. W., KARGER, D. R., KOLLIOPOULOS, S. G., SENGUPTA, S., UMA, R. N., AND WEIN, J. 1998. Techniques for scheduling with rejection. In Proceedings of the 6th Annual European Symposium on Algorithms. G. Bilardi, G. F. Italiano, A. Pietracaprina, and G. Pucci, Eds. Lecture Notes in Computer Science, vol. 1461. Springer, Berlin, Germany, pp. 490-501.
    • (1998) Proceedings of the 6th Annual European Symposium on Algorithms , vol.1461 , pp. 490-501
    • Engels, D.W.1    Karger, D.R.2    Kolliopoulos, S.G.3    Sengupta, S.4    Uma, R.N.5    Wein, J.6
  • 13
    • 85027123851 scopus 로고
    • Approximating the value of two prover proof systems, with applications to max 2SAT and max dicut
    • (Tel-Aviv, Israel, Jan. 4-6). IEEE Computer Society Press, Los Alamitos, Calif.
    • FEIGE, U., AND GOEMANS, M. X. 1995. Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT. In Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems (ISTCS '95) (Tel-Aviv, Israel, Jan. 4-6). IEEE Computer Society Press, Los Alamitos, Calif., pp. 182-189.
    • (1995) Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems (ISTCS '95) , pp. 182-189
    • Feige, U.1    Goemans, M.X.2
  • 14
    • 0346613559 scopus 로고    scopus 로고
    • Improved approximation algorithms for max k-cut and max bisection
    • FRIEZE, A., AND JERRUM, M. 1997. Improved approximation algorithms for MAX k-CUT and MAX BISECTION. Algorithmica 18, 67-81.
    • (1997) Algorithmica , vol.18 , pp. 67-81
    • Frieze, A.1    Jerrum, M.2
  • 16
    • 0000457427 scopus 로고    scopus 로고
    • Semidefinite programming in combinatorial optimization
    • GOEMANS, M. X. 1997b. Semidefinite programming in combinatorial optimization. Math. Prog. 79, 143-161.
    • (1997) Math. Prog. , vol.79 , pp. 143-161
    • Goemans, M.X.1
  • 18
    • 0033733029 scopus 로고    scopus 로고
    • A 1.47-approximation algorithm for a preemptive single-machine scheduling problem
    • GOEMANS, M. X., WEIN, J., AND WILLIAMSON, D. P. 2000. A 1.47-approximation algorithm for a preemptive single-machine scheduling problem. Op. Res. Lett. 26, 149-154.
    • (2000) Op. Res. Lett. , vol.26 , pp. 149-154
    • Goemans, M.X.1    Wein, J.2    Williamson, D.P.3
  • 19
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • GOEMANS, M. X., AND WILLIAMSON, D. P. 1995. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42, 1115-1145.
    • (1995) J. ACM , vol.42 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 20
    • 74849101820 scopus 로고
    • Optimization and approximation in deterministic sequencing and scheduling: A survey
    • GRAHAM, R. L., LAWLER, E. L., LENSTRA, J. K., AND RINNOOY KAN, A. H. G. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Disc. Math. 5, 287-326.
    • (1979) Ann. Disc. Math. , vol.5 , pp. 287-326
    • Graham, R.L.1    Lawler, E.L.2    Lenstra, J.K.3    Rinnooy Kan, A.H.G.4
  • 21
    • 51249185617 scopus 로고
    • The ellipsoid method and its consequences in combinatorial optimization
    • Corrigendum: 4 (1984), 291-295
    • GRÖTSCHEL, M., LOVÁSZ, L., AND SCHRIJVER, A. 1981. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 169-197. (Corrigendum: 4 (1984), 291-295.)
    • (1981) Combinatorica , vol.1 , pp. 169-197
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 23
    • 0031207982 scopus 로고    scopus 로고
    • Scheduling to minimize average completion time: Off-line and on-line approximation algorithms
    • HALL, L. A., SCHULZ, A. S., SHMOYS, D. B., AND WEIN, J. 1997. Scheduling to minimize average completion time: Off-line and on-line approximation algorithms. Math. Op. Res. 22, 513-544.
    • (1997) Math. Op. Res. , vol.22 , pp. 513-544
    • Hall, L.A.1    Schulz, A.S.2    Shmoys, D.B.3    Wein, J.4
  • 25
    • 84958741058 scopus 로고    scopus 로고
    • Non-approximability results for scheduling problems with minsum criteria
    • R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, Eds. Lecture Notes in Computer Science Springer, Berlin
    • HOOGEVEEN, H., SCHUURMAN, P., AND WOEGINGER, G. J. 1998. Non-approximability results for scheduling problems with minsum criteria. In Integer Programming and Combinatorial Optimization, R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, Eds. Lecture Notes in Computer Science, vol. 1412. Springer, Berlin, pp. 353-366.
    • (1998) Integer Programming and Combinatorial Optimization , vol.1412 , pp. 353-366
    • Hoogeveen, H.1    Schuurman, P.2    Woeginger, G.J.3
  • 27
    • 0032028848 scopus 로고    scopus 로고
    • Approximate graph coloring by semidefinite programming
    • KARGER, D., MOTWANI, R., AND SUDAN, M. 1998. Approximate graph coloring by semidefinite programming. J. ACM 45, 2 (Mar.), 246-265.
    • (1998) J. ACM , vol.45 , Issue.2 MAR. , pp. 246-265
    • Karger, D.1    Motwani, R.2    Sudan, M.3
  • 28
    • 0022805963 scopus 로고
    • Worst case bound of an LRF schedule for the mean weighted flow-time problem
    • KAWAGUCHI, T., AND KYAN, S. 1986. Worst case bound of an LRF schedule for the mean weighted flow-time problem. SIAM J. Comput. 15, 1119-1129.
    • (1986) SIAM J. Comput. , vol.15 , pp. 1119-1129
    • Kawaguchi, T.1    Kyan, S.2
  • 29
    • 0141968029 scopus 로고
    • Polynomial solvability of convex quadratic programming
    • KOZLOV, M. K., TARASOV, S. P., AND HAČIJAN, L. G. 1979. Polynomial solvability of convex quadratic programming. Soviet Math. Dok. 20, 1108-1111.
    • (1979) Soviet Math. Dok. , vol.20 , pp. 1108-1111
    • Kozlov, M.K.1    Tarasov, S.P.2    Hačijan, L.G.3
  • 30
    • 0345901561 scopus 로고
    • Sequencing and scheduling: Algorithms and complexity
    • Logistics of Production and Inventory, Chap. 9, S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, Eds. North-Holland, Amsterdam, The Netherlands
    • LAWLER, E. L., LENSTRA, J. K., RINNOOY KAN, A. H. G., AND SHMOYS, D. B. 1993. Sequencing and scheduling: Algorithms and complexity. In Logistics of Production and Inventory, Chap. 9, S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, Eds. Handbooks in Operations Research and Management Science, vol. 4. North-Holland, Amsterdam, The Netherlands, pp. 445-522.
    • (1993) Handbooks in Operations Research and Management Science , vol.4 , pp. 445-522
    • Lawler, E.L.1    Lenstra, J.K.2    Rinnooy Kan, A.H.G.3    Shmoys, D.B.4
  • 32
    • 0000438412 scopus 로고
    • Approximation algorithms for scheduling unrelated parallel machines
    • LENSTRA, J. K., SHMOYS, D. B., AND TARDOS, E. 1990. Approximation algorithms for scheduling unrelated parallel machines. Math. Prog. 46, 259-271.
    • (1990) Math. Prog. , vol.46 , pp. 259-271
    • Lenstra, J.K.1    Shmoys, D.B.2    Tardos, E.3
  • 33
    • 0032620819 scopus 로고    scopus 로고
    • Derandomizing approximation algorithms based on semidefinite programming
    • MAHAJAN, S., AND RAMESH, H. 1999. Derandomizing approximation algorithms based on semidefinite programming. SIAM J. Comput. 28, 1641-1663.
    • (1999) SIAM J. Comput. , vol.28 , pp. 1641-1663
    • Mahajan, S.1    Ramesh, H.2
  • 34
    • 84958053242 scopus 로고    scopus 로고
    • Scheduling jobs with communication delays: Using infeasible solutions for approximation
    • J. Diaz and M. Serna, Eds. Lecture Notes in Computer Science . Springer, Berlin, Germany
    • MÖHRING, R. H., SCHÄFFTER, M. W., AND SCHULZ, A. S. 1996. Scheduling jobs with communication delays: Using infeasible solutions for approximation. In Algorithms - ESA '96, J. Diaz and M. Serna, Eds. Lecture Notes in Computer Science, vol. 1136. Springer, Berlin, Germany, pp. 76-96.
    • (1996) Algorithms - ESA '96 , vol.1136 , pp. 76-96
    • Möhring, R.H.1    Schäffter, M.W.2    Schulz, A.S.3
  • 35
    • 0011423230 scopus 로고    scopus 로고
    • Randomized approximation algorithms in combinatorial optimization
    • Chap. 11. D. S. Hochbaum Ed. Thomson, Boston, Mass.
    • MOTWANI, R., NAOR, J., AND RAGHAVAN, P. 1996. Randomized approximation algorithms in combinatorial optimization. In Approximation algorithms for NP-Hard Problems, Chap. 11. D. S. Hochbaum Ed. Thomson, Boston, Mass., pp. 447-481.
    • (1996) Approximation Algorithms for NP-hard Problems , pp. 447-481
    • Motwani, R.1    Naor, J.2    Raghavan, P.3
  • 37
    • 84958753582 scopus 로고    scopus 로고
    • Approximation bounds for a general class of precedence constrained parallel machine scheduling problems
    • R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, Eds. Lecture Notes in Computer Science . Springer, Berlin, Germany
    • MUNIER, A., QUEYRANNE, M., AND SCHULZ, A. S. 1998. Approximation bounds for a general class of precedence constrained parallel machine scheduling problems. In Integer Programming and Combinatorial Optimization. R. E. Bixby, E. A. Boyd, and R. Z. Ríos-Mercado, Eds. Lecture Notes in Computer Science, vol. 1412. Springer, Berlin, Germany, pp. 367-382.
    • (1998) Integer Programming and Combinatorial Optimization , vol.1412 , pp. 367-382
    • Munier, A.1    Queyranne, M.2    Schulz, A.S.3
  • 39
    • 0025418536 scopus 로고
    • Towards an architecture-independent analysis of parallel algorithms
    • PAPADIMITRIOU, C. H., AND YANNAKAKIS, M. 1990. Towards an architecture-independent analysis of parallel algorithms. SIAM J. Comput. 19, 322-328.
    • (1990) SIAM J. Comput. , vol.19 , pp. 322-328
    • Papadimitriou, C.H.1    Yannakakis, M.2
  • 40
    • 0026366408 scopus 로고
    • Optimization, approximation, and complexity classes
    • PAPADIMITRIOU, C. H., AND YANNAKAKIS, M. 1991. Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43, 425-440.
    • (1991) J. Comput. Syst. Sci. , vol.43 , pp. 425-440
    • Papadimitriou, C.H.1    Yannakakis, M.2
  • 41
    • 0031701702 scopus 로고    scopus 로고
    • Improved bounds on relaxations of a parallel machine scheduling problem
    • PHILLIPS, C., SCHULZ, A. S., SHMOYS, D. B., STEIN, C., AND WEIN, J. 1998. Improved bounds on relaxations of a parallel machine scheduling problem. J. Combin. Opt. 1, 413-426.
    • (1998) J. Combin. Opt. , vol.1 , pp. 413-426
    • Phillips, C.1    Schulz, A.S.2    Shmoys, D.B.3    Stein, C.4    Wein, J.5
  • 43
    • 0041541787 scopus 로고    scopus 로고
    • Minimizing average completion time in the presence of release dates
    • PHILLIPS, C., STEIN, C., AND WEIN, J. 1998. Minimizing average completion time in the presence of release dates. Math. Prog. 82, 199-223.
    • (1998) Math. Prog. , vol.82 , pp. 199-223
    • Phillips, C.1    Stein, C.2    Wein, J.3
  • 44
    • 51249173817 scopus 로고
    • Randomized rounding: A technique for provably good algorithms and algorithmic proofs
    • RAGHAVAN, P., AND THOMPSON, C. D. 1987. Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica 7, 365-374.
    • (1987) Combinatorica , vol.7 , pp. 365-374
    • Raghavan, P.1    Thompson, C.D.2
  • 45
    • 0016883405 scopus 로고
    • Algorithms for scheduling independent tasks
    • SAHNI, S. 1976. Algorithms for scheduling independent tasks. J. ACM 23, 116-127.
    • (1976) J. ACM , vol.23 , pp. 116-127
    • Sahni, S.1
  • 46
  • 47
    • 4243049800 scopus 로고    scopus 로고
    • The power of α-points in preemptive single machine scheduling
    • submitted for publication
    • SCHULZ, A. S., AND SKUTELLA, M. 2001a, The power of α-points in preemptive single machine scheduling. J. Scheduling, submitted for publication.
    • (2001) J. Scheduling
    • Schulz, A.S.1    Skutella, M.2
  • 48
    • 0036662436 scopus 로고    scopus 로고
    • Scheduling unrelated machines by randomized rounding
    • submitted for publication
    • SCHULZ, A. S., AND SKUTELLA, M. 2001b. Scheduling unrelated machines by randomized rounding. SIAM J. Disc. Math., submitted for publication.
    • (2001) SIAM J. Disc. Math.
    • Schulz, A.S.1    Skutella, M.2
  • 49
    • 0042983554 scopus 로고    scopus 로고
    • Polynomial time approximation algorithms for machine scheduling: Ten open problems
    • SCHUURMAN, P., AND WOEGINGER, G. J. 1999. Polynomial time approximation algorithms for machine scheduling: ten open problems. J. Sched. 2, 203-213.
    • (1999) J. Sched. , vol.2 , pp. 203-213
    • Schuurman, P.1    Woeginger, G.J.2
  • 51
    • 0038309442 scopus 로고
    • An approximation algorithm for the generalized assignment problem
    • SHMOYS, D. B., AND TARDOS, E. 1993. An approximation algorithm for the generalized assignment problem. Math. Prog. 62, 461-474.
    • (1993) Math. Prog. , vol.62 , pp. 461-474
    • Shmoys, D.B.1    Tardos, E.2
  • 53
    • 0034138331 scopus 로고    scopus 로고
    • A PTAS for minimizing the total weighted completion time on identical parallel machines
    • SKUTELLA, M., AND WOEGINGER, G. J. 2000. A PTAS for minimizing the total weighted completion time on identical parallel machines. Math. Oper. Res. 25, 63-75.
    • (2000) Math. Oper. Res. , vol.25 , pp. 63-75
    • Skutella, M.1    Woeginger, G.J.2
  • 54
    • 0002066821 scopus 로고
    • Various optimizers for single-stage production
    • SMITH, W. E. 1956. Various optimizers for single-stage production. Nav. Res. Log. Q. 3, 59-66.
    • (1956) Nav. Res. Log. Q. , vol.3 , pp. 59-66
    • Smith, W.E.1
  • 57
    • 0032631766 scopus 로고    scopus 로고
    • Outward rotations: A tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems
    • (Atlanta, Ga., May 1-4). ACM, New York
    • ZWICK, U. 1999. Outward rotations: A tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing (Atlanta, Ga., May 1-4). ACM, New York, pp. 679-687.
    • (1999) Proceedings of the 31st Annual ACM Symposium on Theory of Computing , pp. 679-687
    • Zwick, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.