Random restricted matching and lower bounds for combinatorial optimization
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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.
KeywordsTraveling salesman Minimal spanning tree Voronoi decomposition Restricted matching Packing problems Uniform distribution
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