Minimum augmentation of local edge-connectivity between vertices and vertex subsets in undirected graphs

  • Authors:

  • Toshimasa Ishii;Masayuki Hagiwara

  • Affiliations:

  • Department of Information and Computer Sciences, Toyohashi University of Technology, Aichi, Japan;Fujitsu Ten Technology, Hyogo, Japan

  • Venue:
  • Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

Given an undirected multigraph G = (V, E), a family W of sets W ⊆ V of vertices (areas), and a requirement function r : W → Z+ (where Z+ is the set of nonnegative integers) we consider the problem of augmenting G by the smallest number of new edges so that the resulting graph has at least r(W) edge-disjoint paths between v and W for every pair of a vertex v ∈ V and an area W ∈ W. So far this problem was shown to be NP-hard in the uniform case of r(W) = 1 for each W ∈ W, and polynomially solvable in the uniform case of r(W) = r ≥ 2 for each W ∈ W. In this paper, we show that the problem can be solved in O(m + pn4(r* + logn)) time, even if r(W) ≥ 2 holds for each W ∈ W, where n = |V|, m = |{{u, v}|(u, v) ∈ E}|, p = |W|, and r* = max{r(W)|W ∈ W}.