TY - GEN
T1 - Maximizing symmetric submodular functions
AU - Feldman, Moran
N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
N2 - Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. In this work, we identify submodular maximization problems for which one can get a better approximation for symmetric objectives compared to what is known for general submodular functions. For the problem of maximizing a non-negative symmetric submodular function f: 2 N → R+ subject to a down-monotone solvable polytope P ⊆ [0, 1] N, we describe an algorithm producing a fractional solution of value at least 0.432 · f(OPT), where OPT is the optimal integral solution. Our second result is a 0.432-approximation algorithm for the problem max{f(S): |S| = k} with a non-negative symmetric submodular function f: 2N → R+. Our method also applies to non-symmetric functions, in which case it produces 1/e − o(1) approximation. Finally, we describe a deterministic linear-time 1/2-approximation algorithm for unconstrained maximization of a non-negative symmetric submodular function.
AB - Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. In this work, we identify submodular maximization problems for which one can get a better approximation for symmetric objectives compared to what is known for general submodular functions. For the problem of maximizing a non-negative symmetric submodular function f: 2 N → R+ subject to a down-monotone solvable polytope P ⊆ [0, 1] N, we describe an algorithm producing a fractional solution of value at least 0.432 · f(OPT), where OPT is the optimal integral solution. Our second result is a 0.432-approximation algorithm for the problem max{f(S): |S| = k} with a non-negative symmetric submodular function f: 2N → R+. Our method also applies to non-symmetric functions, in which case it produces 1/e − o(1) approximation. Finally, we describe a deterministic linear-time 1/2-approximation algorithm for unconstrained maximization of a non-negative symmetric submodular function.
KW - Cardinality constraint
KW - Matroid constraint
KW - Symmetric submodular functions
UR - https://www.scopus.com/pages/publications/84945577824
U2 - 10.1007/978-3-662-48350-3_44
DO - 10.1007/978-3-662-48350-3_44
M3 - Conference contribution
SN - 9783662483497
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 521
EP - 532
BT - Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
A2 - Bansal, Nikhil
A2 - Finocchi, Irene
PB - Springer Verlag
T2 - 23rd European Symposium on Algorithms, ESA 2015
Y2 - 14 September 2015 through 16 September 2015
ER -