|
|
|
|
LEADER |
02317 am a22002173u 4500 |
001 |
80848 |
042 |
|
|
|a dc
|
100 |
1 |
0 |
|a Goemans, Michel X.
|e author
|
100 |
1 |
0 |
|a Massachusetts Institute of Technology. Department of Mathematics
|e contributor
|
100 |
1 |
0 |
|a Goemans, Michel X.
|e contributor
|
700 |
1 |
0 |
|a Soto, Jose A.
|e author
|
245 |
0 |
0 |
|a Algorithms for Symmetric Submodular Function Minimization under Hereditary Constraints and Generalizations
|
260 |
|
|
|b Society for Industrial and Applied Mathematics,
|c 2013-09-23T12:47:04Z.
|
856 |
|
|
|z Get fulltext
|u http://hdl.handle.net/1721.1/80848
|
520 |
|
|
|a We present an efficient algorithm to find nonempty minimizers of a symmetric submodular function f over any family of sets I closed under inclusion. Our algorithm makes O(n[superscript 3]) oracle calls to f and I, where n is the cardinality of the ground set. In contrast, the problem of minimizing a general submodular function under a cardinality constraint is known to be inapproximable within o(√n/log n) [Z. Svitkina and L. Fleischer, in Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, IEEE, Washington, DC, 2008, pp. 697--706]. We also present two extensions of the above algorithm. The first extension reports all nontrivial inclusionwise minimal minimizers of f over I using O(n[superscript 3]) oracle calls, and the second reports all extreme subsets of f using O(n[superscript 4]) oracle calls. Our algorithms are similar to a procedure by Nagamochi and Ibaraki [Inform. Process. Lett., 67 (1998), pp. 239--244] that finds all nontrivial inclusionwise minimal minimizers of a symmetric submodular function over a set of size n using O(n[superscript 3]) oracle calls. Their procedure in turn is based on Queyranne's algorithm [M. Queyranne, Math. Program., 82 (1998), pp. 3--12] to minimize a symmetric submodular function by finding pendent pairs. Our results extend to any class of functions for which we can find a pendent pair whose head is not a given element.
|
520 |
|
|
|a National Science Foundation (U.S.) (Contract CCF-0829878)
|
520 |
|
|
|a National Science Foundation (U.S.) (Contrac tCCF-1115849)
|
520 |
|
|
|a United States. Office of Naval Research (Grant N00014-11-1-0053)
|
546 |
|
|
|a en_US
|
655 |
7 |
|
|a Article
|
773 |
|
|
|t SIAM Journal on Discrete Mathematics
|