Greedily finding a dense subgraph

Yuichi Asahiro, Kazuo Iwama, Hisao Tamaki, Takeshi Tokuyama

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

30 Citations (Scopus)

Abstract

Given an n-vertex graph with non-negative edge weights and a positive integer k ≤ n, we are to find a fc-vertex subgraph with the maximum weight. We study the following greedy algorithm for this problem: repeatedly remove a vertex with the minimum weighted-degree in the currently remaining graph, until exactly k vertices are left. We derive tight bounds on the worst case approximation ratio R of this greedy algorithm: (1/2+n/(2k))2-O(1/n) ≤ R ≤ (1/2+n/(2k))2+O(1/n) for k in the range n/3 ≤ k ≤ n and 2(n/k - 1) - O(1/k) ≤ R ≤ 2(n/k - 1) + O(n/k2) for k < n/3. For k = n/2, for example, these bounds are 9/4±O(1/n), improving on naive lower and upper bounds of 2 and 4 respectively. The upper bound for general k shows that this simple algorithm is better than the best previously known algorithm at least by a factor of 2 when k ≥ n11/18.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings
EditorsRolf Karlsson, Andrzej Lingas
PublisherSpringer Verlag
Pages136-148
Number of pages13
ISBN (Print)3540614222, 9783540614227
DOIs
Publication statusPublished - 1996
Event5th Scandinavian Workshop on Algorithm Theory, SWAT 1996 - Reykjavik, Iceland
Duration: 1996 Jul 31996 Jul 5

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1097
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Scandinavian Workshop on Algorithm Theory, SWAT 1996
CountryIceland
CityReykjavik
Period96/7/396/7/5

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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