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 Paper Abstract and Keywords Presentation 2006-05-24 10:40 Minimum Augmentation of Edge-Connectivity with Monotone Requirements in Undirected GraphsToshimasa Ishii (Otaru Univ. of Commerce) Abstract (in Japanese) (See Japanese page) (in English) For a finite ground set $V$, we call a set-function $r: 2^V \rightarrow Z^+$ monotone, if $r(X')\geq r(X)$ holds for each $X' \subseteq X \subseteq V$, where $Z^+$ is the set of nonnegative integers. Given an undirected multigraph $G=(V,E)$ and a monotone requirement function $r: 2^V \rightarrow Z^+$, we consider the problem of augmenting $G$ by a smallest number of new edges so that the resulting graph $G'$ satisfies $d_{G'}(X)\geq r(X)$ for each $\emptyset \neq X \subset V$, where $d_G(X)$ denotes the degree of a vertex set $X$ in $G$. This problem includes the edge-connectivity augmentation problem, and the node-to-area edge-connectivity augmentation problem which is known to be NP-hard. In this paper, we show that the problem can be solved in $O(n^4(m+n\log{n}))$ time under the assumption that each $\emptyset \neq X \subset V$ satisfies $r(X)\geq 2$ whenever $r(X)>0$, where $n=|V|$ and $m=|\{\{u,v\}\mid (u,v)\in E\}|$. Keyword (in Japanese) (See Japanese page) (in English) undirected graph / edge-connectivity / connevtivity augmentation problem / monotone function / / / / Reference Info. IEICE Tech. Rep., vol. 106, no. 63, COMP2006-10, pp. 1-8, May 2006. Paper # COMP2006-10 Date of Issue 2006-05-17 (COMP) ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380 Download PDF

 Conference Information Committee COMP Conference Date 2006-05-24 - 2006-05-24 Place (in Japanese) (See Japanese page) Place (in English) Kyushu Institute of Technology Topics (in Japanese) (See Japanese page) Topics (in English) Paper Information Registration To COMP Conference Code 2006-05-COMP Language English Title (in Japanese) (See Japanese page) Sub Title (in Japanese) (See Japanese page) Title (in English) Minimum Augmentation of Edge-Connectivity with Monotone Requirements in Undirected Graphs Sub Title (in English) Keyword(1) undirected graph Keyword(2) edge-connectivity Keyword(3) connevtivity augmentation problem Keyword(4) monotone function Keyword(5) Keyword(6) Keyword(7) Keyword(8) 1st Author's Name Toshimasa Ishii 1st Author's Affiliation Otaru University of Commerce (Otaru Univ. of Commerce) 2nd Author's Name 2nd Author's Affiliation () 3rd Author's Name 3rd Author's Affiliation () 4th Author's Name 4th Author's Affiliation () 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 1 Date Time 2006-05-24 10:40:00 Presentation Time 35 Registration for COMP Paper # IEICE-COMP2006-10 Volume (vol) IEICE-106 Number (no) no.63 Page pp.1-8 #Pages IEICE-8 Date of Issue IEICE-COMP-2006-05-17