IEICE Technical Committee Submission System
Conference Paper's Information
Online Proceedings
[Sign in]
Tech. Rep. Archives
 Go Top Page Go Previous   [Japanese] / [English] 

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  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  
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 ()
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 

[Return to Top Page]

[Return to IEICE Web Page]

The Institute of Electronics, Information and Communication Engineers (IEICE), Japan