| Paper Abstract and Keywords |
| Presentation |
2006-05-24 10:40
Minimum Augmentation of Edge-Connectivity with Monotone Requirements in Undirected Graphs
Toshimasa 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 |
| Download PDF |
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| 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) |
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| 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) |
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| Keyword(1) |
undirected graph |
| Keyword(2) |
edge-connectivity |
| Keyword(3) |
connevtivity augmentation problem |
| Keyword(4) |
monotone function |
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| 1st Author's Name |
Toshimasa Ishii |
| 1st Author's Affiliation |
Otaru University of Commerce (Otaru Univ. of Commerce) |
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| Speaker |
Author-1 |
| Date Time |
2006-05-24 10:40:00 |
| Presentation Time |
35 minutes |
| Registration for |
COMP |
| Paper # |
COMP2006-10 |
| Volume (vol) |
vol.106 |
| Number (no) |
no.63 |
| Page |
pp.1-8 |
| #Pages |
8 |
| Date of Issue |
2006-05-17 (COMP) |