The External Network Problem with edge- or arc-connectivity requirements

van den Heuvel, Jan; Johnson, Matthew

Abstract

The connectivity of a communications network can often be enhanced if the nodes are able, at some expense, to form links using an external network. In this paper, we consider the problem of how to obtain a prescribed level of connectivity with a minimum number of nodes connecting to the external network. Let D = (V,A) be a digraph. A subset X of vertices in V may be chosen, the so-called external vertices. An internal path is a normal directed path in D; an external path is a pair of internal paths p1=v1 ⋯ vs, p2=w1 ⋯ wt in D such that vs and w1 are external vertices ( the idea is that v1 can contact wt along this path using an external link from vt to w1 ). Then (D,X) is externally-k-arc-strong if for each pair of vertices u and v in V, there are k arc-disjoint paths ( which may be internal or external ) from u to v. We present polynomial algorithms that, given a digraph D and positive integer k, will find a set of external vertices X of minimum size subject to the requirement that (D,X) must be externally-k-arc-strong.

Citation

van den Heuvel, J., & Johnson, M. (2004, August). The External Network Problem with edge- or arc-connectivity requirements. Presented at Combinatorial and Algorithmic Aspects of Networking (CAAN 2004), Banff, Alberta, Canada

• Presentation Conference Type: Conference Paper (published)
• Conference Name: Combinatorial and Algorithmic Aspects of Networking (CAAN 2004)
• Start Date: Aug 5, 2004
• End Date: Aug 7, 2004
• Publication Date: Aug 1, 2005
• Deposit Date: Oct 28, 2008
• Publicly Available Date: Dec 11, 2015
• Print ISSN: 0302-9743
• Pages: 114-126
• Series Title: Lecture notes in computer science
• Series Number: 3405
• Series ISSN: 0302-9743,1611-3349
• Book Title: Combinatorial and algorithmic aspects of networking : first workshop on combinatorial and algorithmic aspects of networking, CAAN 2004, Banff, Alberta, Canada, August 5-7, 2004 ; revised selected papers.
• DOI: https://doi.org/10.1007/11527954_11
• Public URL: https://durham-repository.worktribe.com/output/1162848