Abstract
We prove results on optimal random extensions of trees over points in [0,1]d. As an application, we give a general framework for translating results from combinatorial optimization about the behaviour of random points into results for point sets with sufficiently high regularity. We furthermore introduce a new irregularity problem concerning Voronoi cells, which has applications in logistics.
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This research was supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”.
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Steinerberger, S. Random restricted matching and lower bounds for combinatorial optimization. J Comb Optim 24, 280–298 (2012). https://doi.org/10.1007/s10878-011-9384-4
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DOI: https://doi.org/10.1007/s10878-011-9384-4