Cooperative facility location games

Journal of Algorithms

Volumn 50, Issue 2, 2004, Pages 194-214

  Goemans, Michael X ^a   Skutella, Martin ^b,c  

^a Department of Mathematics ^*  (United States)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Cooperative games; Core; Facility location; LP relaxation; Randomized rounding

Indexed keywords

COMPUTATIONAL COMPLEXITY; COST EFFECTIVENESS; LINEAR PROGRAMMING; OPERATIONS RESEARCH; RESOURCE ALLOCATION; THEOREM PROVING;

COOPERATIVE GAMES; COST ALLOCATION PROBLEM; FACILITY LOCATION; RANDOMIZED ROUNDING;

GAME THEORY;

EID: 1442313867     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-6774(03)00098-1     Document Type: Article

References (42)

1. A.A. Ageev, On the complexity of minimization problems for polynomials in boolean variables, Upravlyaemye Sistemy 23 (1983) 3-11 (in Russian).
2. A.A. Ageev, A criterion of polynomial-time solvability for the network location problem, in: E. Balas, G. Cornuéjols, R. Kannan (Eds.), Integer Programming and Combinational Optimization, Carnegie Mellon Univ., Pittsburgh, 1992, pp. 237-245.
3. R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows. Theory, Algorithms, and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1993.
4. M.L. Balinski, Integer programming: Methods, uses, computation, Manag. Sci. 12 (1965) 253-313.
5. A. Bar-Noy, S. Guha, J. Naor, B. Schieber, Approximating the throughput of multiple machines under real-time scheduling, in: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, 1999, pp. 622-631.
6. I. Bárány, J. Edmonds, L.A. Wolsey, Packing and covering a tree by subtrees, Combinatorica 6 (1986) 221-233.
7. D. Bertsimas, C. Teo, R. Vohra, On dependent randomized rounding algorithms, Oper. Res. Lett. 24 (1999) 105-114.
8. P. Chardaire, Facility location optimization and cooperative games, PhD thesis, University of East Anglia, Norwich, UK, 1998.
9. F.A. Chudak, Improved approximation algorithms for uncapacitated facility location, in: R.E. Bixby, E.A. Boyd, R.Z. Ríos-Mercado (Eds.), Integer Programming and Combinatorial Optimization, in: Lecture Notes Comput. Sci., vol. 1412, Springer-Verlag, Berlin, 1998, pp. 180-194.
10. G. Cornuéjols, G.L. Nemhauser, L.A. Wolsey, The uncapacitated facility location problem, in: P. Mirchandani, R. Francis (Eds.), Discrete Location Theory, Wiley, New York, 1990, pp. 119-171.
11. X. Deng, T. Ibaraki, H. Nagamochi, Algorithmic aspects of the core of combinatorial optimization games, Math. Oper. Res. 24 (1999) 751-766
12. also in: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997.
13. X. Deng, T. Ibaraki, H. Nagamochi, W. Zang, Totally balanced combinatorial optimization games, Math. Program. 87 (2000) 441-452.
14. X. Deng, C.H. Papadimitriou, On the complexity of cooperative solution concepts, Math. Oper. Res. 19 (1994) 257-266.
15. U. Faigle, S.P. Fekete, W. Hochstättler, W. Kern, On the complexity of testing membership in the core of min-cost spanning tree games, Int. J. Game Theory 26 (1997) 361-366.
16. U. Faigle, W. Kern, On the core of ordered submodular cost games, Math. Program. 87 (2000) 483-499.
17. E.K. Gimadi, An effective algorithm for the solution of the location problem with service domains connected with respect to an acyclic network, Upravlyaemye Sistemy 23 (1983) 12-23 (in Russian).
18. M. Göthe-Lundgren, K. Jörnsten, P. Värbrand, On the nucleolus of the basic vehicle routing game, Math. Program. 72 (1996) 83-100.
19. D. Granot, D. Skorin-Karpov, On some optimization problems on k-trees and partial k-trees, Discrete Appl. Math. 48 (1994) 129-145.
20. V.P. Grishukhin, On polynomial solvability conditions for the simplest plant location problem, Trans. Amer. Math. Soc. Ser. 2 158 (1994) 37-46
21. translation from translation from Economico-Mathematical Modelling of Discrete Processes, Moscow, 1988, pp. 52-65.
22. M. Grötschel, L. Lovász, A. Schrijver, Geometric Algorithms and Combinatorial Optimization, in: Algorithms Combin., vol. 2, Springer-Verlag, Berlin, 1988.
23. S. Guha, S. Khuller, Greedy strikes back: Improved facility location algorithms, in: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, pp. 649-657.
24. A. Kolen, Solving covering problems and the uncapacitated plant location problem on trees, Eur. J. Oper. Res. 12 (1983) 266-278.
25. A. Kolen, A. Tamir, Covering problems, in: P. Mirchandani, R. Francisc (Eds.), Discrete Location Theory, Wiley, New York, 1990, pp. 263-304.
26. J. Krarup, O. Bilde, Plant location, set covering and economic lot size: an O (mn)-algorithm for structured problems, in: L. Collatz, W. Wetterling (Eds.), Numerische Methoden bei Optimierungsaufgaben, Band 3 (Optimierung bei graphentheoretischen und ganzzahligen Problemen), in: Int. Ser. Numer. Math., vol. 36, Birkhaüser, 1977, pp. 155-180.
27. J. Lenstra, D. Shmoys, E. Tardos, Approximation algorithms for scheduling unrelated parallel machines, Math. Program. 46 (1990) 259-271.
28. P.B. Mirchandani, P.L. Francis (Eds.), Discrete Location Theory, Wiley, New York, 1990.
29. R. Motwani, P. Raghavan, Randomized Algorithms, Cambridge Univ. Press, Cambridge, UK, 1995.
30. H. Moulin, Cooperative Microeconomics: A Game-Theoretic Introduction, Princetone Univ. Press, Princeton, NJ, 1995.
31. G.L. Nemhauser, L.A. Wolsey, Integer and Combinatorial Optimization, Wiley, New York, 1988.
32. A. Oudjit, Median locations on deterministic and probabilistic multidimensional networks, PhD thesis, Rensselaer Polytechnic Institute, Troy, NJ, 1981.
33. G. Owen, Game Theory, Academic Press, 1995.
34. M. Padberg, Linear Optimization and Extensions, Springer-Verlag, Berlin, 1995.
35. D. Samet, E. Zemet, On the core and dual set of linear programming games, Math. Oper. Res. 9 (1984) 309-316.
36. W.W. Sharkey, Cores of games with fixed costs and shared facilities, Internat. Econom. Rev. 31 (1990) 245-262.
37. D.B. Shmoys, E. Tardos, An approximation algorithm for the generalized assignment problem, Math. Program. 62 (1993) 461-474.
38. A. Tamir, On the core of cost allocation games denned on location problems, Transp. Sci. 27 (1992) 81-86
39. also in: Proceedings of the International Symposium on Locational Decisions, Skodsborg, Denmark, 1981.
40. V.A. Trubin, An effective algorithm for solving the distribution problem in a network in the form of a tree, Soviet Math. Dokl. 17 (1976) 1604-1608
41. translation from: translation from Dokl. Akad. Nauk SSSR 231 (1976) 547-550.
42. V.V. Vaziani, Approximation Algorithms, Springer-Verlag, Berlin, 2001.