The Complexity of Multiterminal Cuts
SIAM Journal on Computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Information Processing Letters
Multiway cuts in node weighted graphs
Journal of Algorithms
Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut
Mathematics of Operations Research
Greedy splitting algorithms for approximating multiway partition problems
Mathematical Programming: Series A and B
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Approximating submodular functions everywhere
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Facility location with hierarchical facility costs
ACM Transactions on Algorithms (TALG)
Symmetry and Approximability of Submodular Maximization Problems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Submodular Function Minimization under Covering Constraints
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximability of Combinatorial Problems with Multi-agent Submodular Cost Functions
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Finding minimum 3-way cuts in hypergraphs
Information Processing Letters
The Design of Approximation Algorithms
The Design of Approximation Algorithms
Computing minimum multiway cuts in hypergraphs from hypertree packings
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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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 f1, ... , fk on V. The objective is to partition V into k (possibly empty) sets A1, ... , Ak such that the sum Σi=1k fi(Ai) 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 convexprogramming 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), HΔ}-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 nodeweighted multiway cut problem in graphs.