494 research outputs found

    Computing a Minimum-Cost kk-hop Steiner Tree in Tree-Like Metrics

    Get PDF
    We consider the problem of computing a Steiner tree of minimum cost under a kk-hop constraint which requires the depth of the tree to be at most kk. Our main result is an exact algorithm for metrics induced by graphs of bounded treewidth that runs in time nO(k)n^{O(k)}. For the special case of a path, we give a simple algorithm that solves the problem in polynomial time, even if kk is part of the input. The main result can be used to obtain, in quasi-polynomial time, a near-optimal solution that violates the kk-hop constraint by at most one hop for more general metrics induced by graphs of bounded highway dimension

    Sparse Euclidean Spanners with Optimal Diameter: A General and Robust Lower Bound via a Concave Inverse-Ackermann Function

    Get PDF
    • …
    corecore