approximation and hardness results for label cut and related problems

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	approximation and hardness results for label cut and related problems
	Zhang Peng; Cai Jin-Yi; Tang Lin-Qing; Zhao Wen-Bo
	2011
Source	Journal of Combinatorial Optimization
ISSN	13826905
Volume	21 Issue:2 Pages:192-208
English Abstract	We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t, the edges of G are classified into different categories, represented by a set of labels. The labels may also have weights. We want to pick a subset of labels of minimum cardinality (or minimum total weight), such that the removal of all edges with these labels disconnects s and t. We give the first non-trivial approximation and hardness results for the Label Cut problem. Firstly, we present an O(m) -approximation algorithm for the Label Cut problem, where m is the number of edges in the input graph. Secondly, we show that it is NP-hard to approximate Label Cut within 2^{log 1-1 / log log c}nn for any constant c<1/2, where n is the input length of the problem. Thirdly, our techniques can be applied to other previously considered optimization problems. In particular we show that the Minimum Label Path problem has the same approximation hardness as that of Label Cut, simultaneously improving and unifying two known hardness results for this problem which were previously the best (but incomparable due to different complexity assumptions). © 2009 Springer Science+Business Media, LLC.
Indexed Type	ei
Keyword	Combinatorial Optimization Hardness
Department	(1) School of Computer Science and Technology, Shandong University, Ji'nan 250101, China; (2) Computer Sciences Department, University of Wisconsin, Madison, WI 53706, United States; (3) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China; (4) Graduate University, Chinese Academy of Sciences, Beijing 100190, China; (5) Dept. of Computer Science and Engineering, University of California, San Diego, San Diego, CA 92093, United States
Language	英语
Content Type	期刊论文
URI	http://ir.iscas.ac.cn/handle/311060/14065
Collection	中国科学院软件研究所
Recommended Citation GB/T 7714	Zhang Peng,Cai Jin-Yi,Tang Lin-Qing,et al. approximation and hardness results for label cut and related problems[J]. Journal of Combinatorial Optimization,2011,21(2):192-208.
APA	Zhang Peng,Cai Jin-Yi,Tang Lin-Qing,&Zhao Wen-Bo.(2011).approximation and hardness results for label cut and related problems.Journal of Combinatorial Optimization,21(2),192-208.
MLA	Zhang Peng,et al."approximation and hardness results for label cut and related problems".Journal of Combinatorial Optimization 21.2(2011):192-208.

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