Max-and min-neighborhood monopolies

Kazuhisa Makino, Masafumi Yamashita, Tiko Kameda

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

1 Citation (Scopus)

Abstract

Given a graph G = (V,E) and a set of vertices M ⊑ V, a vertex v ϵ V is said to be controlled by M if the majority of v's neighbors (including itself) belongs to M. M is called a monopoly if every vertex v ϵ V is controlled by M. For a specified M and a range for E (E1 ⊑ E ⊑ E2), we try to determine E such that M is a monopoly in G = (V,E). We first present a polynomial algorithm for testing if such an E exists, by formulating it as a network flow problem. Assuming that a solution E does exist, we then show that a solution with the maximum or minimum |E| can be found in polynomial time, by considering them as weighted matching problems. In case there is no solution E, we want to maximize the number of vertices controlled by the given M. Unfortunately, this problem turns out to be NP-hard. We therefore design a simple approximation algorithm which guarantees an approximation ratio of 2.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
EditorsMagnús M. Halldórsson
PublisherSpringer Verlag
Pages513-526
Number of pages14
ISBN (Print)3540676902, 9783540676904
DOIs
Publication statusPublished - Jan 1 2000
Event7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway
Duration: Jul 5 2000Jul 7 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1851
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th Scandinavian Workshop on Algorithm Theory, SWAT 2000
CountryNorway
CityBergen
Period7/5/007/7/00

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Makino, K., Yamashita, M., & Kameda, T. (2000). Max-and min-neighborhood monopolies. In M. M. Halldórsson (Ed.), Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings (pp. 513-526). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1851). Springer Verlag. https://doi.org/10.1007/3-540-44985-X