The balanced edge cover problem

Yuta Harada, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

For an undirected graph G∈=∈(V, E), an edge cover is defined as a set of edges that covers all vertices of V. It is known that a minimum edge cover can be found in polynomial time and forms a collection of star graphs. In this paper, we consider the problem of finding a balanced edge cover where the degrees of star center vertices are balanced, which can be applied to optimize sensor network structures, for example. To this end, we formulate the problem as a minimization of the summation of strictly monotone increasing convex costs associated with degrees for covered vertices, and show that the optimality can be characterized as the non-existence of certain alternating paths. By using this characterization, we show that the optimal covers are also minimum edge covers, have the lexicographically smallest degree sequence of the covered vertices, and minimize the maximum degree of covered vertices. Based on the characterization we also present an O(|V||E|) time algorithm.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 19th International Symposium, ISAAC 2008, Proceedings
Pages246-257
Number of pages12
DOIs
Publication statusPublished - Dec 1 2008
Event19th International Symposium on Algorithms and Computation, ISAAC 2008 - Gold Coast, QLD, Australia
Duration: Dec 15 2008Dec 17 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5369 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th International Symposium on Algorithms and Computation, ISAAC 2008
CountryAustralia
CityGold Coast, QLD
Period12/15/0812/17/08

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Harada, Y., Ono, H., Sadakane, K., & Yamashita, M. (2008). The balanced edge cover problem. In Algorithms and Computation - 19th International Symposium, ISAAC 2008, Proceedings (pp. 246-257). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5369 LNCS). https://doi.org/10.1007/978-3-540-92182-0_24