On generalized greedy splitting algorithms for multiway partition problems

Authors:
Liang Zhao;Hiroshi Nagamochi;Toshihide Ibaraki
Affiliations:
Department of Information Science, Faculty of Engineering, Utsunomiya University, Yoto 7-1-2, Utsunomiya 321-8585, Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 9
Cited 0

Combinatorial algorithms for integrated circuit layout

Combinatorial algorithms for integrated circuit layout
An efficient K-way graph partitioning algorithm for task allocation in parallel computing systems

ISCI '90 Proceedings of the first international conference on systems integration on Systems integration '90
A polynomial algorithm for the k-cut problem for fixed k

Mathematics of Operations Research
The Complexity of Multiterminal Cuts

SIAM Journal on Computing
Finding $k$ Cuts within Twice the Optimal

SIAM Journal on Computing
Rounding algorithms for a geometric embedding of minimum multiway cut

STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On Minimum 3-Cuts and Approximating k-Cuts Using Cut Trees

Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Multiway Cuts in Directed and Node Weighted Graphs

ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
A new and improved algorithm for the 3-cut problem

Operations Research Letters

Quantified Score

Hi-index	0.05

Visualization

Abstract

Given a system (V,T,f,k) where V is a finite set, T ⊆ V, f : 2V → R is a submodular function and k ≥ 2 is an integer, the multiway partition problem (MPP) asks to find a k-partition P = {V1, V2,...,Vk} of V that satisfies Vi ∩ T ≠ 0 for all i and minimizes f(V1) + f(V2)+...+f(Vk). This formulation captures a generalization of many NP-hard partition problems in graphs or hypergraphs. Previously, the authors have shown a simple framework for approximating MPPs by greedily increasing the size of partition by one. In this paper, we show that, if T = V, improved guarantees are available by greedily increasing the size by two. We also show polynomial time implementations for several problem classes.