On constant time approximation of parameters of bounded degree graphs

Noga Alon*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


How well can the maximum size of an independent set, or the minimum size of a dominating set of a graph in which all degrees are at most d be approximated by a randomized constant time algorithm ? Motivated by results and questions of Nguyen and Onak, and of Parnas, Ron and Trevisan, we show that the best approximation ratio that can be achieved for the first question (independence number) is between Ω(d/logd) and O(d loglogd/ logd), whereas the answer to the second (domination number) is (1 + o(1)) ln d.

Original languageEnglish
Title of host publicationProperty Testing - Current Research and Surveys
Number of pages6
StatePublished - 2010
EventMini-Workshop on Property Testing - Beijing, China
Duration: 8 Jan 201010 Jan 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6390 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceMini-Workshop on Property Testing


  • constant time approximation
  • dominating set in a graph
  • independence number of a graph


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