On efficient distance approximation for graph properties

Nimrod Fiat, Dana Ron

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

6 Scopus citations

Abstract

A distance-approximation algorithm for a graph property P in the adjacency-matrix model is given an approximation parameter ε ∈ (0, 1) and query access to the adjacency matrix of a graph G = (V, E). It is required to output an estimate of the distance between G and the closest graph G0 = (V, E0) that satisfies P, where the distance between graphs is the size of the symmetric difference between their edge sets, normalized by |V |2. In this work we introduce property covers, as a basis for a methodology that uses distance-approximation algorithms for “simple” properties to design distance-approximation algorithms for more “complex” properties. Applying this methodology we present distance-approximation algorithms with poly(1/ε) query complexity for induced P3-freeness, induced P4-freeness, and Chordality. For induced C4-freeness our algorithm has query complexity exp(poly(1/ε)). These complexities essentially match the corresponding known results for testing these properties and provide an exponential improvement on previously known results.

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2021
EditorsDaniel Marx
PublisherAssociation for Computing Machinery
Pages1618-1637
Number of pages20
ISBN (Electronic)9781611976465
StatePublished - 2021
Event32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States
Duration: 10 Jan 202113 Jan 2021

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/TerritoryUnited States
CityAlexandria, Virtual
Period10/01/2113/01/21

Funding

FundersFunder number
Israel Science Foundation1146/18

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