Constrained Submodular Maximization via a Nonsymmetric Technique
Published Online:17 May 2019https://doi.org/10.1287/moor.2018.0955
References
- [1] (1999) An 0.828 approximation algorithm for the uncapacitated facility location problem. Discrete Appl. Math. 93(2/3):149–156.Crossref, Google Scholar
- [2] (2000) The Probabilistic Method, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
- [3] (2016) Better balance by being biased: A 0.8776-approximation for max bisection. ACM Trans. Algorithms 13(1):2.Crossref, Google Scholar
- [4] (2013) Learning with submodular functions: A convex optimization perspective. Foundations Trends Machine Learn. 6(2/3):145–373.Crossref, Google Scholar
- [5] (2001) Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. Proc. 8th IEEE Internat. Conf. Comput. Vision, vol. 1 (IEEE, Piscataway, NJ), 105–112.Crossref, Google Scholar
- [6] (2015) A tight linear time (1/2)-approximation for unconstrained submodular maximization. SIAM J. Comput. 44(5):1384–1402.Crossref, Google Scholar
- [7] (2014) Submodular maximization with cardinality constraints. Proc. 25th Annual ACM-SIAM Sympos. Discrete Algorithms, Portland, Oregon, 1433–1452.Crossref, Google Scholar
- [8] (2011) Maximizing a monotone submodular function subject to a matroid constraint. SIAM J. Comput. 40(6):1740–1766.Crossref, Google Scholar
- [9] (2011) Approximation algorithms for submodular multiway partition. IEEE 52nd Annual Sympos. Foundations Comput. Sci. (IEEE, Piscataway, NJ), 807–816.Crossref, Google Scholar
- [10] (2005) A polynomial time approximation scheme for the multiple knapsack problem. SIAM J. Comput. 35(3):713–728.Crossref, Google Scholar
- [11] (2010) Dependent randomized rounding via exchange properties of combinatorial structures. IEEE 51st Annual Sympos. Foundations Comput. Sci. (IEEE, Piscataway, NJ), 575–584.Crossref, Google Scholar
- [12] (2014) Submodular function maximization via the multilinear relaxation and contention resolution schemes. SIAM J. Comput. 43(6):1831–1879.Crossref, Google Scholar
- [13] (2006) An efficient approximation for the generalized assignment problem. Inform. Processing Lett. 100(4):162–166.Crossref, Google Scholar
- [14] (1984) Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem. Discrete Appl. Math. 7(3):251–274.Crossref, Google Scholar
- [15] (1977) Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms. Management Sci. 23(8):789–810.Link, Google Scholar
- [16] (1977) On the uncapacitated location problem. Ann. Discrete Math. 1:163–177.Crossref, Google Scholar
- [17] (2016) Constrained submodular maximization: Beyond 1/e. Proc. 57th Annual Sympos. Foundations Comput. Sci. (IEEE, Piscataway, NJ), 248–257.Crossref, Google Scholar
- [18] (1998) A threshold of lnn for approximating set cover. J. ACM 45(4):634–652.Crossref, Google Scholar
- [19] (1995) Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT. Proc. 3rd Israel Sympos. Theory Comput. Systems (IEEE, Piscataway, NJ), 182–189.Crossref, Google Scholar
- [20] (2006) Approximation algorithms for allocation problems: Improving the factor of 1–1/e. 47th Annual IEEE Sympos. Foundations Comput. Sci. (IEEE, Piscataway, NJ), 667–676.Crossref, Google Scholar
- [21] (2011) Maximizing non-monotone submodular functions. SIAM J. Comput. 40(4):1133–1153.Crossref, Google Scholar
- [22] (2013) Maximization problems with submodular objective functions. Unpublished PhD thesis, Technion–Israel Institute of Technology, Haifa, Israel.Google Scholar
- [23] (2011) A unified continuous greedy algorithm for submodular maximization. Proc. 52nd Annual Sympos. Foundations Comput. Sci. (IEEE, Piscataway, NJ), 570–579.Crossref, Google Scholar
- [24] (2011) Improved approximations for k-exchange systems. Demetrescu C, Halldórsson MM, eds. Algorithms—ESA 2011: Proc. 19th Annual European Sympos., Lecture Notes in Computer Science, vol. 6942 (Springer, Berlin), 784–798.Google Scholar
- [25] (1978) An analysis of approximations for maximizing submodular set functions–II. Polyhedral Combinatorics, Mathematical Programming Studies, vol. 8 (Springer, Berlin), 73–87.Crossref, Google Scholar
- [26] (2006) Tight approximation algorithms for maximum general assignment problems. Proc. 17th Annual ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 611–620.Crossref, Google Scholar
- [27] (1995) Improved approximation algorithms for MAX k-CUT and MAX BISECTION. Balas E, Clausen J, eds. Proc. 18th Internat. Conf. Integer Program. Combinatorial Optimization, Lecture Notes in Computer Science, vol. 920 (Springer, Berlin), 1–13.Google Scholar
- [28] (2011) Submodular maximization by simulated annealing. Proc. 22nd Annual ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 1098–1117.Crossref, Google Scholar
- [29] (1995) Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6):1115–1145.Crossref, Google Scholar
- [30] (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatoria 1(2):169–197.Crossref, Google Scholar
- [31] (2001) Combinatorial approximation algorithms for the maximum directed cut problem. Proc. 12th Annual ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 1–7.Google Scholar
- [32] (2008) Optimal marketing strategies over social networks. Proc. 17th Internat. Conf. World Wide Web (ACM, New York), 189–198.Crossref, Google Scholar
- [33] (2001) Some optimal inapproximability results. J. ACM 48(4):798–859.Crossref, Google Scholar
- [34] (1978) K-greedy algorithms for independence systems. Oper. Res. Ser. A-B 22(1):219–228.Google Scholar
- [35] (1980) Worst case analysis of greedy type algorithms for independence systems. Math. Programming Stud. 12:120–131.Crossref, Google Scholar
- [36] (2011) Submodularity beyond submodular energies: Coupling edges in graph cuts. Proc. 2011 IEEE Conf. Comput. Vision Pattern Recognition (IEEE, Piscataway, NJ), 1897–1904.Crossref, Google Scholar
- [37] (1976) The efficacy of the greedy algorithm. Cong. Num. 17:341–350.Google Scholar
- [38] (1972) Reducibility among combinatorial problems. Miller RE, Thatcher JW, eds. Complexity of Computer Computations (Plenum Press, New York), 85–103.Crossref, Google Scholar
- [39] (2003) Maximizing the spread of influence through a social network. Proc. 9th ACM SIGKDD Internat. Conf. Knowledge Discovery Data Mining (ACM, New York), 137–146.Crossref, Google Scholar
- [40] (2007) Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? SIAM J. Comput. 37(1):319–357.Crossref, Google Scholar
- [41] (1999) The budgeted maximum coverage problem. Inform. Processing Lett. 70(1):39–45.Crossref, Google Scholar
- [42] (1978) An analysis of the greedy heuristic for independence systems. Ann. Discrete Math. 2:65–74.Crossref, Google Scholar
- [43] (2008) Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies. J. Machine Learn. Res. 9:235–284.Google Scholar
- [44] (2005) Near-optimal nonmyopic value of information in graphical models. Proc. 21st Conf. Uncertainty Artificial Intelligence, 5.Google Scholar
- [45] (2008) Efficient sensor placement optimization for securing large water distribution networks. J. Water Resources Planning Management 134(6):516–526.Crossref, Google Scholar
- [46] (2013) Approximations for monotone and nonmonotone submodular maximization with knapsack constraints. Math. Oper. Res. 38(4):729–739.Link, Google Scholar
- [47] (2010) Submodular maximization over multiple matroids via generalized exchange properties. Math. Oper. Res. 35(4):795–806.Link, Google Scholar
- [48] (2010) Maximizing non-monotone submodular functions under matroid or knapsack constraints. SIAM J. Discrete Math. 23(4):2053–2078.Crossref, Google Scholar
- [49] (2010) Multi-document summarization via budgeted maximization of submodular functions. Proc. 2010 Annual Conf. North Amer. Chapter Assoc. Comput. Linguistics/Human Language Tech. (ACM, Stroudsburg, PA).Google Scholar
- [50] (2011) A class of submodular functions for document summarization. Proc. 49th Annual Meeting Assoc. Comput. Linguistics: Human Language Tech. (Association for Computational Linguistics, Stroudsburg, PA), 510–520.Google Scholar
- [51] (1983) Submodular functions and convexity. Bachem A, Grötschel M, Korte B, eds. Mathematical Programming: The State of the Art (Springer-Verlag, Berlin, Heidelberg), 235–257.Crossref, Google Scholar
- [52] (1978) Best algorithms for approximating the maximum of a submodular set function. Math. Oper. Res. 3(3):177–188.Link, Google Scholar
- [53] (1978) An analysis of approximations for maximizing submodular set functions—I. Math. Programming 14(1):265–294.Crossref, Google Scholar
- [54] (2004) A note on maximizing a submodular set function subject to knapsack constraint. Oper. Res. Lett. 32(1):41–43.Crossref, Google Scholar
- [55] (2000) Gadgets, approximation, and linear programming. SIAM J. Comput. 29(6):2074–2097.Crossref, Google Scholar
- [56] (2013) Symmetry and approximability of submodular maximization problems. SIAM J. Comput. 42(1):265–304.Crossref, Google Scholar

