Greedy splitting algorithms for approximating multiway partition problems

Abstract. Given a system (V, T, f, k), where V is a finite set, T ⊆ V , f : 2 → R is a submodular function and k ≥ 2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition P = {V1, V2, . . ., Vk} of V that satisfies Vi∩T 6= ∅ for all i and minimizes f(V1)+f(V2)+ · · ·+f(Vk), where P is a k-partition of V if (i) Vi 6= ∅, (ii) Vi ∩ Vj = ∅, i 6= j, and (iii) V1 ∪ V2 ∪ · · · ∪ Vk = V hold. MPP formulation captures a generalization in submodular systems of many NP-hard problems such as k-way cut, multiterminal cut, target split and their generalizations in hypergraphs. This paper presents a simple and unified framework for developing and analyzing approximation algorithms for various MPPs.