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Testing versus estimation of graph properties

Published: 22 May 2005 Publication History

Abstract

The topic of tolerant property testing, that of distinguishing input instances that are far from satisfying a property from those that are close enough to satisfying it (as opposed to distinguishing the far instances only from the satisfying instances), has recently become an active topic of research in the field of combinatorial property testing [13]. In the general setting, there exist properties that are testable but not tolerantly testable [10]. However, we show here that in the setting of the dense graph model, all testable properties are not only tolerantly testable, but also admit a constant query size algorithm that estimates the distance from the property up to any fixed additive constant.In the course of the construction of this algorithm we develop a framework for extending Szemerédi's Regularity Lemma, both as a prerequisite for formulating what kind of information about the input graph will provide us with the correct estimation, and as the means for efficiently gathering this information. This work is also connected to the question of finding a combinatorial characterization of the testable graph properties, and to the question of efficiently finding a regular partition.

References

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  • (2019)Testing whether a digraph contains H-free k-induced subgraphsTheoretical Computer Science10.1016/j.tcs.2008.08.033407:1-3(545-553)Online publication date: 5-Jan-2019
  • (2017)Testing Hereditary Properties of Ordered Graphs and Matrices2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2017.83(848-858)Online publication date: Oct-2017
  • (2013)Non-Deterministic Graph Property TestingCombinatorics, Probability and Computing10.1017/S096354831300020522:05(749-762)Online publication date: 3-Jul-2013
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cover image ACM Conferences
STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
May 2005
778 pages
ISBN:1581139608
DOI:10.1145/1060590
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 22 May 2005

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Author Tags

  1. distance approximation
  2. graph properties
  3. property testing
  4. regularity lemma

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STOC05
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STOC05: Symposium on Theory of Computing
May 22 - 24, 2005
MD, Baltimore, USA

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