Approximation Algorithms for Submodular Multiway Partition

Abstract— We study algorithms for the SUBMODULAR MULTIWAY PARTITION problem (SUB-MP). An instance of SUB-MP consists of a finite ground set V , a subset S = {s1, s2, . . . , sk} ⊆ V of k elements called terminals, and a non-negative submodular set function f : 2V → R+ on V provided as a value oracle. The goal is to partition V into k sets A1, . . . , Ak to minimize k i=1 f(Ai) such that for 1 ≤ i ≤ k, si ∈ Ai. SUB-MP generalizes some well-known problems such as the MULTIWAY CUT problem in graphs and hypergraphs, and the NODE-WEIGHED MULTIWAY CUT problem in graphs. SUB-MP for arbitrary submodular functions (instead of just symmetric functions) was considered by Zhao, Nagamochi and Ibaraki [29]. Previous algorithms were based on greedy splitting and divide and conquer strategies. In recent work [5] we proposed a convex-programming relaxation for SUB-MP based on the Lov´asz-extension of a submodular function and showed its applicability for some special cases. In this paper ...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Chandra Chekuri, Alina Ene
• Keywords: CORR 2011, Education, Partition Problem, Programming Relaxation, S1 S2