Algorithmic aspects of property testing in the dense graphs model

Oded Goldreich*, Dana Ron

*Corresponding author for this work

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

Abstract

In this paper we consider two basic questions regarding the query complexity of testing graph properties in the adjacency matrix model. The first question refers to the relation between adaptive and non-adaptive testers, whereas the second question refers to testability within complexity that is inversely proportional to the proximity parameter, denoted ε. The study of these questions reveals the importance of algorithmic design in this model. The highlights of our study are: - A gap between the complexity of adaptive and non-adaptive testers. Specifically, there exists a natural graph property that can be tested using Õ(ε-1) adaptive queries, but cannot be tested using Õ(ε-3/2) non-adaptive queries. - In contrast, there exist natural graph properties that can be tested using Õ(ε-1) non-adaptive queries, whereas Ω(ε -1) queries are required even in the adaptive case. We mention that the properties used in the foregoing conflicting results have a similar flavor, although they are of course different.

Original languageEnglish
Title of host publicationProperty Testing - Current Research and Surveys
Pages295-305
Number of pages11
DOIs
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

Conference

ConferenceMini-Workshop on Property Testing
Country/TerritoryChina
CityBeijing
Period8/01/1010/01/10

Keywords

  • Adaptivity vs. Non-adaptivity
  • Graph Properties

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