TY - GEN

T1 - On efficient distance approximation for graph properties

AU - Fiat, Nimrod

AU - Ron, Dana

N1 - Publisher Copyright:
Copyright © 2021 by SIAM

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85105341259&partnerID=8YFLogxK

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AN - SCOPUS:85105341259

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1618

EP - 1637

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

A2 - Marx, Daniel

PB - Association for Computing Machinery

T2 - 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

Y2 - 10 January 2021 through 13 January 2021

ER -