21,762 research outputs found

    Serve or Skip: The Power of Rejection in Online Bottleneck Matching

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    We consider the online matching problem, where n server-vertices lie in a metric space and n request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex.We focus on the egalitarian bottleneck objective, where the goal is to minimize the maximum distance between any request and its server. It has been demonstrated that while there are effective algorithms for the utilitarian objective (minimizing total cost) in the resource augmentation setting where the offline adversary has half the resources, these are not effective for the egalitarian objective. Thus, we propose a new Serve-or-Skip bicriteria analysis model, where the online algorithm may reject or skip up to a specified number of requests, and propose two greedy algorithms: GRI NN(t) and GRIN(t) . We show that the Serve-or-Skip model of resource augmentation analysis can essentially simulate the doubled-server capacity model, and then examine the performance of GRI NN(t) and GRIN(t)

    Higher-Order Triangular-Distance Delaunay Graphs: Graph-Theoretical Properties

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    We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set PP of points in the plane. In TD-Delaunay, the convex distance is defined by a fixed-oriented equilateral triangle â–½\triangledown, and there is an edge between two points in PP if and only if there is an empty homothet of â–½\triangledown having the two points on its boundary. We consider higher-order triangular-distance Delaunay graphs, namely kk-TD, which contains an edge between two points if the interior of the homothet of â–½\triangledown having the two points on its boundary contains at most kk points of PP. We consider the connectivity, Hamiltonicity and perfect-matching admissibility of kk-TD. Finally we consider the problem of blocking the edges of kk-TD.Comment: 20 page
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