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Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs

  • Chandra Chekuri
  • Alina Ene
  • Ali Vakilian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)

Abstract

We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undirected graph G = (V,E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum node-weighted subgraph H of G such that, for each pair uv, H contains r(uv) edge-disjoint paths between u and v. Our main result is an O(k)-approximation algorithm for EC-SNDP where k =  max uv r(uv) is the maximum requirement. This improves the O(k logn)-approximation known for node-weighted EC-SNDP in general graphs [15]. Our algorithm and analysis applies to the more general problem of covering a proper function with maximum requirement k. Our result is inspired by, and generalizes, the work of Demaine, Hajiaghayi and Klein [5] who gave constant factor approximation algorithms for node-weighted Steiner tree and Steiner forest problems (and more generally covering 0-1 proper functions) in planar and minor-closed families of graphs.

Keywords

Planar Graph Steiner Tree Steiner Tree Problem Blue Edge Special Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chandra Chekuri
    • 1
  • Alina Ene
    • 1
  • Ali Vakilian
    • 1
  1. 1.Dept. of Computer ScienceUniversity of IllinoisUrbanaUSA

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