Submodular Maximization over Multiple Matroids via Generalized Exchange Properties

Published Online:https://doi.org/10.1287/moor.1100.0463

References

  • Ageev A., Sviridenko M. Pipage rounding: A new method of constructing algorithms with proven performance guarantee. J. Combin. Optim. (2004) 8(3):307–328CrossrefGoogle Scholar
  • Arkin E., Hassin R. On local search for weighted k-set packing. Math. Oper. Res. (1998) 23(3):640–648LinkGoogle Scholar
  • Berman P. A d/2 approximation for maximum weight independent set in d-claw free graphs. Nordic J. Comput. (2000) 7(3):178–184Google Scholar
  • Brylawski T. Some properties of basic families of subsets. Discrete Math. (1973) 6:333–341CrossrefGoogle Scholar
  • Calinescu G., Chekuri C., Pál M., Vondrák J. Maximizing a submodular set function subject to a matroid constraint. Proc. 12th Internat. Workshop on Integer Programming and Combinat. Optim. (IPCO 2007) (2007) Ithaca, NY:182–196Google Scholar
  • Calinescu G., Chekuri C., Pál M., Vondrák J. Maximizing a submodular set function subject to a matroid constraint. SIAM J. Comp. (2010) . ForthcomingGoogle Scholar
  • Chandra B., Halldórsson M. Greedy local improvement and weighted set packing approximation. J. Algorithms (2001) 39(2):223–240CrossrefGoogle Scholar
  • Conforti M., Cornuéjols G. Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem. Discrete Appl. Math. (1984) 7(3):251–274CrossrefGoogle Scholar
  • Cornuéjols G., Fischer M., Nemhauser G. Location of bank accounts to optimize float: An analytic study of exact and approximation algorithms. Management Sci. (1977a) 23(8):789–810LinkGoogle Scholar
  • Cornuéjols G., Fischer M., Nemhauser G. On the uncapacitated location problem. Ann. Discrete Math. (1977b) 1:163–178CrossrefGoogle Scholar
  • Feige U. A threshold of ln n for approximating set cover. J. ACM (1998) 45:634–652CrossrefGoogle Scholar
  • Feige U., Mirrokni V., Vondrák J. Maximizing non-monotone submodular functions. Proc. 48th Annual IEEE Sympos. on Foundations of Comput. Sci. (FOCS 2007) (2007) 461–471CrossrefGoogle Scholar
  • Fisher M., Nemhauser G., Wolsey L. An analysis of approximations for maximizing submodular set functions—II. Math. Programming Stud. (1978) 8:73–87CrossrefGoogle Scholar
  • Greene C. A multiple exchange property for bases. Proc. Amer. Math. Soc. (1973) 39:45–50CrossrefGoogle Scholar
  • Greene C., Magnanti T. Some abstract pivot algorithms. SIAM J. Appl. Math. (1975) 29:530–539CrossrefGoogle Scholar
  • Hausmann D., Korte B. K-greedy algorithms for independence systems. Zeitschrift Oper. Res. Ser. A–B (1978) 22(5Google Scholar
  • Hausmann D., Korte B., Jenkyns T. Worst case analysis of greedy type algorithms for independence systems. Math. Programming Stud. (1980) 12:120–131CrossrefGoogle Scholar
  • Hazan E., Safra S., Schwartz O. On the complexity of approximating k-set packing. Comput. Complexity (2006) 15(1):20–39CrossrefGoogle Scholar
  • Hurkens C., Schrijver A. On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM J. Discrete Math. (1989) 2(1):68–72CrossrefGoogle Scholar
  • Iwata S., Fleischer L., Fujishige S. A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions. J. ACM (2001) 48:761–777CrossrefGoogle Scholar
  • Jenkyns T. The efficacy of the greedy algorithm. Congressus Numerantium (1976) 17:341–350Google Scholar
  • Lazebnik F., Ustimenko V., Woldar A. A new series of dense graphs of high girth. Bull. Amer. Math. Soc. (1995) 32(1):73–79CrossrefGoogle Scholar
  • Lee J., Sviridenko M., Vondrák J. Submodular maximization over multiple matroids via generalized exchange properties. Proc. 12th Internat. Workshop on Approximation Algorithms for Combinat. Optim. Problems (APPROX 2009) (2009) (Springer, New York) 244–257CrossrefGoogle Scholar
  • Lee J., Mirrokni V., Nagarajan V., Sviridenko M. Maximizing non-monotone submodular functions under matroid and knapsack constraints. SIAM J. Discrete Math. (2010) 23(4):2053–2078(Preliminary version appeared in STOC 2009)CrossrefGoogle Scholar
  • Lovász L., Bachem A., Grötschel M., Korte B. Submodular functions and convexity. Mathematical Programmming—The State of the Art. Proc. 11th Internat. Sympos. on Math. Programming (1983) (Springer-Verlag, Berlin) 234–257CrossrefGoogle Scholar
  • Nemhauser G., Wolsey L. Best algorithms for approximating the maximum of a submodular set function. Math. Oper. Res. (1978) 3(3):177–188LinkGoogle Scholar
  • Nemhauser G., Wolsey L., Fisher M. An analysis of approximations for maximizing submodular set functions—I. Math. Programming (1978) 14:265–294CrossrefGoogle Scholar
  • Oveis-Gharan S., Vondrák J. Submodular maximization by simulated annealing. ACM-SIAM Sympos. on Discrete Algorithms (SODA 2011) (2011) . ForthcomingGoogle Scholar
  • Oxley J.Matroid Theory (1992) (Oxford University Press, New York) Google Scholar
  • Reichel J., Skutella M. Evolutionary algorithms and matroid optimization problems. Genetic and Evolutionary Comput. Conf. (GECCO 2007) (2007) 947–954CrossrefGoogle Scholar
  • Schrijver A. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. J. Combin. Theory, Ser. B (2000) 80:346–355CrossrefGoogle Scholar
  • Schrijver A.Combinatorial Optimization: Polyhedra and Efficiency (2003) (Springer, Berlin) Google Scholar
  • Vondrák J. Optimal approximation for the submodular welfare problem in the value oracle model. Proc. 40th Annual ACM Sympos. Theory of Comput. (STOC 2008) (2008) 67–74CrossrefGoogle Scholar
  • Vondrák J. Symmetry and approximability of submodular maximization problems. Proc. 50th Annual Sympos. on Foundations of Comput. Sci. (FOCS 2009) (2009) 651–670CrossrefGoogle Scholar
  • Woodall D. An exchange theorem for bases of matroids. J. Combin. Theory, Ser. B (1974) 16:227–228CrossrefGoogle Scholar
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