We study the Minimum Submodular-Cost Allocation problem (MSCA). In this problem we are given a finite ground set V and k non-negative submodular set functions f 1,....,f k on V. The objective is to partition V into k (possibly empty) sets A 1,⋯, A k such that the sum ∑i=1k f i (A i ) is minimized. Several well-studied problems such as the non-metric facility location problem, multiway-cut in graphs and hypergraphs, and uniform metric labeling and its generalizations can be shown to be special cases of MSCA. In this paper we consider a convex-programming relaxation obtained via the Lovász-extension for submodular functions. This allows us to understand several previous relaxations and rounding procedures in a unified fashion and also develop new formulations and approximation algorithms for related problems. In particular, we give a (1.5 - 1/k)-approximation for the hypergraph multiway partition problem. We also give a min {2(1 - 1/k), H Δ}- approximation for the hypergraph multiway cut problem when Δ is the maximum hyperedge size. Both problems generalize the multiway cut problem in graphs and the hypergraph cut problem is approximation equivalent to the node-weighted multiway cut problem in graphs. © 2011 Springer-Verlag.
CITATION STYLE
Chekuri, C., & Ene, A. (2011). Submodular cost allocation problem and applications. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6755 LNCS, pp. 354–366). https://doi.org/10.1007/978-3-642-22006-7_30
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