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Random walks and forbidden minors II: a poly(d ε^-1)-query tester for minor-closed properties of bounded degree graphs

Authors:

C. Seshadhri, and

Andrew StolmanAuthors Info & Claims

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

June 2019

Pages 559 - 567

https://doi.org/10.1145/3313276.3316330

Published: 23 June 2019 Publication History

Abstract

Let G be a graph with n vertices and maximum degree d. Fix some minor-closed property P (such as planarity). We say that G is ε-far from P if one has to remove ε dn edges to make it have P. The problem of property testing P was introduced in the seminal work of Benjamini-Schramm-Shapira (STOC 2008) that gave a tester with query complexity triply exponential in ε⁻¹. Levi-Ron (TALG 2015) have given the best tester to date, with a quasipolynomial (in ε⁻¹) query complexity. It is an open problem to get property testers whose query complexity is (dε⁻¹), even for planarity.

In this paper, we resolve this open question. For any minor-closed property, we give a tester with query complexity d· (ε⁻¹). The previous line of work on (independent of n, two-sided) testers is primarily combinatorial. Our work, on the other hand, employs techniques from spectral graph theory. This paper is a continuation of recent work of the authors (FOCS 2018) analyzing random walk algorithms that find forbidden minors.

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Cited By

Romero MWrochna MŽivný S(2023)Pliability and Approximating Max-CSPsJournal of the ACM10.1145/362651570:6(1-43)Online publication date: 30-Nov-2023
https://dl.acm.org/doi/10.1145/3626515
Adriaens FApers S(2023)Testing Cluster Properties of Signed GraphsProceedings of the ACM Web Conference 202310.1145/3543507.3583213(49-59)Online publication date: 30-Apr-2023
https://dl.acm.org/doi/10.1145/3543507.3583213
Chen XRandolph TServedio RSun T(2022)A Lower Bound on Cycle-Finding in Sparse DigraphsACM Transactions on Algorithms10.1145/341797918:4(1-23)Online publication date: 10-Oct-2022
https://dl.acm.org/doi/10.1145/3417979
Show More Cited By

Index Terms

Random walks and forbidden minors II: a poly(d ε^-1)-query tester for minor-closed properties of bounded degree graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Streaming, sublinear and near linear time algorithms

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cover image ACM Conferences

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

June 2019

1258 pages

ISBN:9781450367059

DOI:10.1145/3313276

General Chair:
Moses Charikar
Stanford University
,
Program Chair:
Edith Cohen
Google, USA / Tel Aviv University, Israel

Copyright © 2019 ACM.

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Publication History

Published: 23 June 2019

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STOC '19

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SIGACT

STOC '19: 51st Annual ACM SIGACT Symposium on the Theory of Computing

June 23 - 26, 2019

AZ, Phoenix, USA

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Cited By

Romero MWrochna MŽivný S(2023)Pliability and Approximating Max-CSPsJournal of the ACM10.1145/362651570:6(1-43)Online publication date: 30-Nov-2023
https://dl.acm.org/doi/10.1145/3626515
Adriaens FApers S(2023)Testing Cluster Properties of Signed GraphsProceedings of the ACM Web Conference 202310.1145/3543507.3583213(49-59)Online publication date: 30-Apr-2023
https://dl.acm.org/doi/10.1145/3543507.3583213
Chen XRandolph TServedio RSun T(2022)A Lower Bound on Cycle-Finding in Sparse DigraphsACM Transactions on Algorithms10.1145/341797918:4(1-23)Online publication date: 10-Oct-2022
https://dl.acm.org/doi/10.1145/3417979
Adler IKöhler NPeng PMarx D(2021)On testability of first-order properties in bounded-degree graphsProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458160(1578-1597)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458160
Romero MWrochna MŽivný SMarx D(2021)Treewidth-pliability and PTAS for max-CSPsProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458093(473-483)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458093
Adler IKöhler NPeng P(2021)GSF-locality is not sufficient for proximity-oblivious testingProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.34Online publication date: 20-Jul-2021
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2021.34

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