Efficient Connectivity Testing of Hypercubic Networks with Faults
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.
KeywordsConnected Graph Interconnection Network Graph Class Local Connectivity Isoperimetric Problem
Unable to display preview. Download preview PDF.