research-article

Parameterized Testability

Authors:

Yuichi YoshidaAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 9, Issue 4

Article No.: 16, Pages 1 - 16

https://doi.org/10.1145/3155294

Published: 14 December 2017 Publication History

Abstract

This article studies property testing for NP optimization problems with parameter k under the general graph model with an augmentation of random edge sampling capability. It is shown that a variety of such problems, including k-Vertex Cover, k-Feedback Vertex Set, k-Multicut, k-Path-Free, and k-Dominating Set, are constant-query testable if k is constant. It should be noted that the first four problems are fixed parameter tractable (FPT) and it turns out that algorithmic techniques for their FPT algorithms (branch-and-bound search, color coding, etc.) are also useful for our testers. k-Dominating Set is W[2]-hard, but we can still test the property with a constant number of queries, since the definition of ε-farness makes the problem trivial for non-sparse graphs that are the source of hardness for the original optimization problem. We also consider k-Odd Cycle Transversal, which is another well-known FPT problem, but we only give a sublinear-query tester when k is a constant.

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Cited By

Bishnu AGhosh AKolay SMishra GSaurabh S(2023)Almost optimal query algorithm for hitting set using a subset queryJournal of Computer and System Sciences10.1016/j.jcss.2023.02.002Online publication date: Apr-2023
https://doi.org/10.1016/j.jcss.2023.02.002
Chen HYoshida YSuciu DSkritek SKoch C(2019)Testability of Homomorphism InadmissibilityProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319679(365-382)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319679

Index Terms

Parameterized Testability
1. Theory of computation
  1. Design and analysis of algorithms
    1. Parameterized complexity and exact algorithms
      1. Fixed parameter tractability
    2. Streaming, sublinear and near linear time algorithms
      1. Sketching and sampling

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cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 9, Issue 4

December 2017

105 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/3171589

Editor:
Venkatesan Guruswami
Carnegie Mellon University, USA

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Copyright © 2017 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 December 2017

Accepted: 01 October 2017

Revised: 01 May 2017

Received: 01 August 2016

Published in TOCT Volume 9, Issue 4

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Cited By

Bishnu AGhosh AKolay SMishra GSaurabh S(2023)Almost optimal query algorithm for hitting set using a subset queryJournal of Computer and System Sciences10.1016/j.jcss.2023.02.002Online publication date: Apr-2023
https://doi.org/10.1016/j.jcss.2023.02.002
Chen HYoshida YSuciu DSkritek SKoch C(2019)Testability of Homomorphism InadmissibilityProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319679(365-382)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319679

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