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 |
|
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 |
() |
19th Author's Name |
|
19th Author's Affiliation |
() |
20th Author's Name |
|
20th Author's Affiliation |
() |
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) |
|