Augmenting Local Edge-Connectivity between Vertices and Vertex Subsets in Undirected Graphs

Ishii, Toshimasa; Hagiwara, Masayuki

doi:10.1007/978-3-540-45138-9_43

Cited by 3 publications

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The concept of such connectivity and/or flow-amount between a vertex and a set of specified vertices was given by Ito [9], in the context of considering the design of a reliable telephone network with plural switching apparatuses. Moreover, recently, not only location problems but also connectivity augmentation problems based on this type of connectivity have been studied [6,8,15].…”

Section: Introductionmentioning

confidence: 99%

Minimum cost source location problem with local 3-vertex-connectivity requirements

Ishii

Fujita

Nagamochi

2007

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

Let G = (V, E) be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex v ∈ V has a demand d(v) ∈ Z + and a cost c(v) ∈ R + , where Z + and R + denote the set of nonnegative integers and the set of nonnegative reals, respectively. The source location problem with vertex-connectivity requirements in a given graph G requires finding a set S of vertices minimizing v∈S c(v) such that there are at least d(v) pairwise vertex-disjoint paths from S to v for each vertex v ∈ V − S. It is known that if there exists a vertex v ∈ V with d(v) ≥ 4, then the problem is NP-hard even in the case where every vertex has a uniform cost. In this paper, we show that the problem can be solved in O(|V | 4 log 2 |V |) time if d(v) ≤ 3 holds for each vertex v ∈ V .

show abstract

Section: Introductionmentioning

confidence: 99%