Testing the (s,t)-disconnectivity of graphs and digraphs

Authors:
Yuichi Yoshida;Yusuke Kobayashi
Affiliations:
School of Informatics, Kyoto University, Kyoto 606-8501, Japan and Preferred Infrastructure, Tokyo 113-0033, Japan;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

Property testing is concerned with constant-time algorithms for deciding whether a given object satisfies a predetermined property or is far from satisfying it. In this paper, we consider testing properties related to the connectivity of two vertices in sparse graphs. We present one-sided error testers for (s,t)-disconnectivity with query complexity 2^O^(^1^/^@e^) for digraphs and O(1/@e^2) for graphs, where @e is an error parameter. Furthermore, we show that these algorithms are the best possible in view of query complexity, i.e., we give matching lower bounds for two-sided error testers for both cases. We also give a constant-time algorithm for testing the (s,t)-disconnectivity of a directed bounded-degree hypergraph, which can be used to test the satisfiability of Horn SAT.