Relationship between Approximability and request structures in the minimum certificate dispersal problem

Tomoko Izumi, Taisuke Izumi, Hirotaka Ono, Koichi Wada

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

Given a graph G=(V,E) and a set R ⊆ V ×V of requests, we consider to assign a set of edges to each node in G so that for every request (u, v) in R the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinality of the edge set assigned to each node. In this paper, we give an advanced investigation about the difficulty of MCD by focusing on the relationship between its (in)approximability and request structures. We first show that MCD with general R has Θ(logn) lower and upper bounds on approximation ratio under the assumption P≠NP, where n is the number of nodes in G. We then assume R forms a clique structure, called Subset-Full, which is a natural setting in the context of the application. Interestingly, under this natural setting, MCD becomes to be 2-approximable, though it has still no polynomial time approximation algorithm whose factor better than 677/676 unless P=NP. Finally, we show that this approximation ratio can be improved to 3/2 for undirected variant of MCD with Subset-Full.

本文言語英語
ホスト出版物のタイトルComputing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings
ページ56-65
ページ数10
DOI
出版ステータス出版済み - 2009
イベント15th Annual International Conference on Computing and Combinatorics, COCOON 2009 - Niagara Falls, NY, 米国
継続期間: 7 13 20097 15 2009

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5609 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他15th Annual International Conference on Computing and Combinatorics, COCOON 2009
国/地域米国
CityNiagara Falls, NY
Period7/13/097/15/09

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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