SFO: A Toolbox for Submodular Function Optimization
The Journal of Machine Learning Research
Submodular cost allocation problem and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
SIAM Journal on Computing
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Given a system (V,T,f,k), where V is a finite set, ** is a submodular function and k≥2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition ** ={V1,V2,...,Vk} of V that satisfies ** for all i and minimizes f(V1)+f(V2)+···+f(Vk), where ** is a k-partition of ** 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.