Tight Approximation for Partial Vertex Cover with Hard Capacities
碩士 === 國立臺灣大學 === 電子工程學研究所 === 106 === We consider the partial vertex cover problem with hard capacity constraints (Partial VC-HC) on hypergraphs. In this problem we are given a hypergraph G=(V,E) with a maximum edge size f and a covering requirement R. Each edge is associated with a demand, and eac...
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ndltd-TW-106NTU054281202019-07-25T04:46:49Z http://ndltd.ncl.edu.tw/handle/xm4jfv Tight Approximation for Partial Vertex Cover with Hard Capacities 考慮嚴格容積的部分頂點覆蓋問題之最佳近似演算法 Jia-Yau Shiau 蕭家堯 碩士 國立臺灣大學 電子工程學研究所 106 We consider the partial vertex cover problem with hard capacity constraints (Partial VC-HC) on hypergraphs. In this problem we are given a hypergraph G=(V,E) with a maximum edge size f and a covering requirement R. Each edge is associated with a demand, and each vertex is associated with a capacity and an (integral) available multiplicity. The objective is to compute a minimum vertex multiset such that at least R units of demand from the edges are covered by the capacities of the vertices in the multiset and the multiplicity of each vertex does not exceed its available multiplicity. In this thesis we present an f-approximation for this problem, improving over a previous result of (2f+2)(1+ϵ) by Cheung et al. to the tightest extent possible. Our new ingredient of this work is a generalized analysis on the extreme points of the natural LP, developed from previous works, and a strengthened LP lower-bound obtained for the optimal solutions. Der-Tsai Lee 李德財 2018 學位論文 ; thesis 41 en_US |
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碩士 === 國立臺灣大學 === 電子工程學研究所 === 106 === We consider the partial vertex cover problem with hard capacity constraints (Partial VC-HC) on hypergraphs. In this problem we are given a hypergraph G=(V,E) with a maximum edge size f and a covering requirement R. Each edge is associated with a demand, and each vertex is associated with a capacity and an (integral) available multiplicity. The objective is to compute a minimum vertex multiset such that at least R units of demand from the edges are covered by the capacities of the vertices in the multiset and the multiplicity of each vertex does not exceed its available multiplicity.
In this thesis we present an f-approximation for this problem, improving over a previous result of (2f+2)(1+ϵ) by Cheung et al. to the tightest extent possible. Our new ingredient of this work is a generalized analysis on the extreme points of the natural LP, developed from previous works, and a strengthened LP lower-bound obtained for the optimal solutions.
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Der-Tsai Lee |
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Der-Tsai Lee Jia-Yau Shiau 蕭家堯 |
author |
Jia-Yau Shiau 蕭家堯 |
spellingShingle |
Jia-Yau Shiau 蕭家堯 Tight Approximation for Partial Vertex Cover with Hard Capacities |
author_sort |
Jia-Yau Shiau |
title |
Tight Approximation for Partial Vertex Cover with Hard Capacities |
title_short |
Tight Approximation for Partial Vertex Cover with Hard Capacities |
title_full |
Tight Approximation for Partial Vertex Cover with Hard Capacities |
title_fullStr |
Tight Approximation for Partial Vertex Cover with Hard Capacities |
title_full_unstemmed |
Tight Approximation for Partial Vertex Cover with Hard Capacities |
title_sort |
tight approximation for partial vertex cover with hard capacities |
publishDate |
2018 |
url |
http://ndltd.ncl.edu.tw/handle/xm4jfv |
work_keys_str_mv |
AT jiayaushiau tightapproximationforpartialvertexcoverwithhardcapacities AT xiāojiāyáo tightapproximationforpartialvertexcoverwithhardcapacities AT jiayaushiau kǎolǜyángéróngjīdebùfēndǐngdiǎnfùgàiwèntízhīzuìjiājìnshìyǎnsuànfǎ AT xiāojiāyáo kǎolǜyángéróngjīdebùfēndǐngdiǎnfùgàiwèntízhīzuìjiājìnshìyǎnsuànfǎ |
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1719230367624331264 |