@MISC{Gregora_testingconnectivity, author = {Petr Gregora and Tomasz Radzikb}, title = {Testing connectivity of faulty networks in sublinear timeI}, year = {} }

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Abstract

Given a set F of vertices of a connected graph G, we study the problem of testing the connectivity of G−F in polynomial time with respect to |F | and the maximum degree ∆ of G. We present two approaches. The first algorithm for this problem runs in O (|F |∆2ε−1 log(|F |∆ε−1)) time for every graph G with vertex expansion at least ε> 0. The other solution, designed for the class of graphs with cycle basis consisting of cycles of length at most l, leads to O (|F |∆dl/2e log(|F |∆bl/2c)) running time. We also present an extension of this method to test the biconnectivity of G − F in O (|F |∆l log(|F |∆l)) time.