G =(V,E), a specified set of vertices Γ V, a subgraph G ′=(V,E ′) with λ(Γ;G ′) = k of G and a cost function c: E Z+ (nonnegative integers), find a set E* E - E ′of edges, each connecting distinct vertices of V, of minimum total cost such that λ(Γ;G″) k + δ for G"=(V,E ′∪E*)," where λ(Γ;G″) is the minimum value of the maximum number of edge disjoint paths between any pair of vertices in Γ of G". The paper proposes an O(Δ+|V||E|) time 2-approximation algorithm FSAR for (k + 1)ECA-SV with a restriction λ(V;G ′) = λ(Γ;G ′), where Δ is the time complexity of constructing a structural graph of a given graph G ′." />

A 2-Approximation Algorithm to (k + 1)-Edge-Connect a Specified Set of Vertices in a k-Edge-Connected Graph

Toshiya MASHIMA  Satoshi TAOKA  Toshimasa WATANABE 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E88-A  No.5  pp.1290-1300
Publication Date: 2005/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
graphs,  augmentation problems,  edge-connectivity,  approximation algorithms, 

Full Text: PDF(389.2KB)

Summary: 
The (k + δ)-edge-connectivity augmentation problem for a specified set of vertices ((k + δ)ECA-SV) is defined as follows: "Given an undirected graph G =(V,E), a specified set of vertices Γ V, a subgraph G ′=(V,E ′) with λ(Γ;G ′) = k of G and a cost function c: E Z+ (nonnegative integers), find a set E* E - E ′of edges, each connecting distinct vertices of V, of minimum total cost such that λ(Γ;G″) k + δ for G"=(V,E ′∪E*)," where λ(Γ;G″) is the minimum value of the maximum number of edge disjoint paths between any pair of vertices in Γ of G". The paper proposes an O(Δ+|V||E|) time 2-approximation algorithm FSAR for (k + 1)ECA-SV with a restriction λ(V;G ′) = λ(Γ;G ′), where Δ is the time complexity of constructing a structural graph of a given graph G ′.