Fast algorithms for parametric scheduling come from extensions to parametric maximum flow

Operations Research

Volumn 47, Issue 5, 1999, Pages 744-756

  Mccormick, S Thomas ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; JOB ANALYSIS; MATHEMATICAL MODELS; PROBLEM SOLVING;

GALLO METHODS; PARAMETRIC MAXIMUM FLOW PROBLEM; PARAMETRIC SCHEDULING;

SCHEDULING;

EID: 0033337360     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.47.5.744     Document Type: Article

References (28)

1. Ahuja, R. K., T. L. Magnanti, J. B. Orlin. 1993. Network Flows: Theory, Algorithms and Applications. Prentice Hall, New York.
2. _, J. B. Orlin, C. Stein, R. E. Tarjan. 1994. Improved algorithms for bipartite network flow. SIAM J. Comput. 23 906-933.
3. Arai, T., S. Ueno, Y. Kajitani. 1993. Generalization of a theorem on the parametric maximum flow problem. Discrete Appl. Math. 41 69-74.
4. Brumelle, S., D. Granot, L. Liu. 1995a. An extended economic selection problem. Manuscript, University of British Columbia Faculty of Commerce, Vancouver, BC, Canada.
5. _, _, _. 1995b. Totally ordered optimal solutions and parametric maximum flows. Manuscript, University of British Columbia Faculty of Commerce, Vancouver, BC, Canada.
6. Chen, Y. L. 1994. Scheduling jobs to minimize total cost. European J. Oper. Res. 74 111-119.
7. Dinkelbach, W. 1967. On nonlinear fractional programming. Management Sci. 13 492-498.
8. Federgruen, A., H. Groenevelt. 1986. Preemptive scheduling of uniform machines by ordinary network flow techniques. Management Sci. 32 341-349.
9. Fujishige, S. 1991. Submodular Functions and Optimization. Ann. Discrete Math., Vol. 47. North-Holland, Amsterdam.
10. Gallo, G., M. D. Grigoriadis, R. E. Tarjan. 1989. A fast parametric maximum-flow algorithm and applications. SIAM J. Comput. 18 30-55.
11. Garey, M. R., D. S. Johnson. 1979. Computers and Intractability, A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York.
12. Goldberg, A. V., R. E. Tarjan. 1988. A new approach to the maximum flow problem. JACM 35(4) 921-940.
13. Gusfield, D., C. Martel. 1992. A fast algorithm for the generalized parametric minimum cut problem and applications. Algorithmica 7 499-519.
14. Hall, N. G., R. V. Vohra. 1993. Towards equitable distribution via proportional equity constraints. Math. Prog. 58 287-294.
15. Hochbaum, D. S., S-P. Hong. 1995. About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Math. Programming 69 269-309.
16. Hoffman, A., J. Rivlin. 1967. When is a team "mathematically" eliminated? H. W. Kuhn, ed. Princeton Symposium on Math. Programming. Princeton University Press, Princeton, NJ.
17. Horn, W. A. 1974. Some simple scheduling algorithms. Naval Res. Logistics Quart. 21 177-185.
18. Irving, R. W., P. Leather, D. Gusfield. 1987. An efficient algorithm for the "optimal" stable marriage. J. ACM 34 532-543.
19. Iwata, S., T. Matsui, S. T. McCormick. 1998. A fast bipartite network flow algorithm for selective assembly. Oper. Res. Letters 22 137-143.
20. Lawler, E. L., J. K. Lenstra, A. H. G. Rinooy Kan, D. B. Shmoys. 1993. Sequencing and scheduling: algorithms and complexity. S. C. Graves, A. H. G. Rinooy Kan, P. Zipkin, eds. Handbooks in Operations Research and Management Science, Volume 4, Chapter 9. North-Holland, Amsterdam.
21. McCormick, S. T., L. Liu. 1993. An experimental implementation of the dual cancel and tighten algorithm for minimum cost network flow. D. S. Johnson, C. S. McGeoch, eds. Network Flows and Matching. American Mathematical Society DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 12, American Mathematical Society, Providence, RI, 247-266.
22. _, J. Sahni, T. Stewart. 1997. A computational study of algorithms for finding ultimate contours of open-pit mines. Working paper.
23. Megiddo, N. 1983. Applying parallel computation algorithms in the design of serial algorithms. J. ACM 30 852-865.
24. Radzik, T. 1992. Newton's method for fractional combinatorial optimization. Proc. 33rd IEEE Annual Sympos. of Foundations of Computer Sci. 659-669;
25. see also parametric flows, weighted means of cuts, and fractional combinatorial optimization. 1993. P. Pardalos, ed. Complexity in Numerical Optimization, World Scientific, 351-386.
26. Schwartz, B. 1966. Possible winners in partially completed tournaments. SIAM Rev. 8 302-308.
27. Serafini, P. 1996. Scheduling jobs on several machines with the job splitting property. Oper. Res. 44 617-628.
28. Topkis, D. M. 1978. Minimizing a submodular function on a lattice. Oper. Res. 26 305-321.