Abstract
Given a connected graph G and a set F of faulty vertices of G, let G − F be the graph obtained from G by deletion of all vertices of F and edges incident with them. Is there an algorithm, whose running time may be bounded by a polynomial function of |F| and log|V(G)|, which decides whether G − F is still connected? Even though the answer to this question is negative in general, we describe an algorithm which resolves this problem for the n-dimensional hypercube in time O(|F|n3). Furthermore, we sketch a more general algorithm that is efficient for graph classes with good vertex expansion properties.
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Dvořák, T., Fink, J., Gregor, P., Koubek, V., Radzik, T. (2011). Efficient Connectivity Testing of Hypercubic Networks with Faults. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_19
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DOI: https://doi.org/10.1007/978-3-642-19222-7_19
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