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Parameterized Testability

Published:14 December 2017Publication History
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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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      • Published in

        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
        Issue’s Table of Contents

        Copyright © 2017 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 14 December 2017
        • Accepted: 1 October 2017
        • Revised: 1 May 2017
        • Received: 1 August 2016
        Published in toct Volume 9, Issue 4

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