Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varying the spray length and spray angle from a position external to the coating drum. Additionally, this invention provides adjustment means for removing the fixture containing the spray nozzles entirely from the coating drum and laterally from the coating apparatus housing for purging.

[1]  L. Wolsey.  Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems , 1982, Math. Oper. Res..

[2]  U. Feige,et al.  Maximizing Non-monotone Submodular Functions , 2011 .

[3]  Rajiv Gandhi,et al.  Dependent rounding and its applications to approximation algorithms , 2006, JACM.

[4]  N. Alon,et al.  The Probabilistic Method, Second Edition , 2000 .

[5]  Oded Schwartz,et al.  On the complexity of approximating k-set packing , 2006, computational complexity.

[6]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[7]  Maxim Sviridenko,et al.  A note on maximizing a submodular set function subject to a knapsack constraint , 2004, Oper. Res. Lett..

[8]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .

[9]  Alexander Schrijver,et al.  A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time , 2000, J. Comb. Theory, Ser. B.

[10]  Laurence A. Wolsey,et al.  Best Algorithms for Approximating the Maximum of a Submodular Set Function , 1978, Math. Oper. Res..

[11]  Chandra Chekuri,et al.  A recursive greedy algorithm for walks in directed graphs , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[12]  Aranyak Mehta,et al.  Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions , 2005, Algorithmica.

[13]  Vahab S. Mirrokni,et al.  Non-monotone submodular maximization under matroid and knapsack constraints , 2009, STOC '09.

[14]  Sanjeev Khanna,et al.  A PTAS for the multiple knapsack problem , 2000, SODA '00.

[15]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[16]  Vahab S. Mirrokni,et al.  Tight approximation algorithms for maximum general assignment problems , 2006, SODA '06.

[17]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[18]  J. G. Pierce,et al.  Geometric Algorithms and Combinatorial Optimization , 2016 .

[19]  Sanjeev Khanna,et al.  A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem , 2005, SIAM J. Comput..

[20]  Shahar Dobzinski,et al.  An improved approximation algorithm for combinatorial auctions with submodular bidders , 2006, SODA '06.

[21]  Cristina G. Fernandes,et al.  A New Approximation Algorithm for Finding Heavy Planar Subgraphs , 2003, Algorithmica.

[22]  Samir Khuller,et al.  The Budgeted Maximum Coverage Problem , 1999, Inf. Process. Lett..

[23]  Amit Kumar,et al.  Maximum Coverage Problem with Group Budget Constraints and Applications , 2004, APPROX-RANDOM.

[24]  Jan Vondrák,et al.  Symmetry and Approximability of Submodular Maximization Problems , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[25]  Hadas Shachnai,et al.  Maximizing submodular set functions subject to multiple linear constraints , 2009, SODA.

[26]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[27]  Gagan Goel,et al.  On the Approximability of Budgeted Allocations and Improved Lower Bounds for Submodular Welfare Maximization and GAP , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[28]  Jan Vondrák,et al.  Submodular Maximization over Multiple Matroids via Generalized Exchange Properties , 2009, Math. Oper. Res..

[29]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[30]  Vahab S. Mirrokni,et al.  Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions , 2008, EC '08.

[31]  B. Korte,et al.  An Analysis of the Greedy Heuristic for Independence Systems , 1978 .

[32]  Jan Vondrák,et al.  Optimal approximation for the submodular welfare problem in the value oracle model , 2008, STOC.

[33]  Satoru Iwata,et al.  A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions , 2000, STOC '00.

[34]  Uriel Feige,et al.  On maximizing welfare when utility functions are subadditive , 2006, STOC '06.

[35]  Andreas S. Schulz,et al.  Revisiting the Greedy Approach to Submodular Set Function Maximization , 2007 .

[36]  William H. Cunningham,et al.  Testing membership in matroid polyhedra , 1984, J. Comb. Theory, Ser. B.

[37]  Jack Edmonds,et al.  Submodular Functions, Matroids, and Certain Polyhedra , 2001, Combinatorial Optimization.

[38]  Laurence A. Wolsey,et al.  An analysis of the greedy algorithm for the submodular set covering problem , 1982, Comb..

[39]  Satoru Iwata,et al.  A combinatorial strongly polynomial algorithm for minimizing submodular functions , 2001, JACM.

[40]  V. Rich.  Personal communication , 1989, Nature.

[41]  Maxim Sviridenko,et al.  Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee , 2004, J. Comb. Optim..

[42]  Julián Mestre,et al.  Greedy in Approximation Algorithms , 2006, ESA.

[43]  Uriel Feige,et al.  Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[44]  Jan Vondrák,et al.  Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract) , 2007, IPCO.

[45]  Aravind Srinivasan,et al.  Distributions on level-sets with applications to approximation algorithms , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.