A Polynomial Time Algorithm for Almost Optimal Vertex Fault Tolerant Spanners
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We present the first polynomial time algorithm for the f vertex fault tolerant spanner problem, which achieves almost optimal spanner size. Our algorithm for constructing f vertex fault tolerant spanner takes O(k· n· m^2 · W) time, where W is the maximum edge weight, and constructs a spanner of size O(n^1+1/kf^1-1/k· (log n)^1-1/k). Our spanner has almost optimal size and is at most a log n factor away from the upper bound on the worst-case size. Prior to this work, no other polynomial time algorithm was known for constructing f vertex fault tolerant spanner with optimal size. Our algorithm is based on first greedily constructing a hitting set for the collection of paths of weight at most k · w(u,v) between the endpoints u and v of an edge (u,v) and then using this set to decide whether the edge (u,v) needs to be added to the growing spanner.
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