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Fast Algorithms for Diameter-Optimally Augmenting Paths and Trees

    https://doi.org/10.1142/S0129054119500060Cited by:2 (Source: Crossref)

    We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input graph is a path, running in O(nlog3n) time, and (ii) the input graph is a tree, running in O(n2logn) time. We also present an algorithm for paths that computes a (1+𝜀)-approximation in O(n+1/𝜀3) time.

    Communicated by Marek Chrobak

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