We consider the one-round Voronoi game, where the first player ("White", called "Wilma") places a set of n points in a rectangular area Q of aspect ratio r 1, followed by the second player ("Black", called "Barney"), who places the same number of points. Each player wins the fraction of Q closest to one of his points, and the goal is to win more than half of the total area. This problem has been studied by Cheong et al. who showed that for large enough n and r = 1, Barney has a strategy that guarantees a fraction of 1=2+a, for some small fixed a.

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We describe algorithmic results on two crucial aspects of allocating resources on computational hardware devices with partial reconfigurability. By using methods from the field of computational geometry, we derive a method that allows correct maintainance of free and occupied space of a set of n rectangular modules in time O(nlog n); previous approaches needed a time of O(n 2) for correct results and O(n) for heuristic results. We also show a matching lower bound of Ω(n log n), so our approach is optimal. We also show that finding an optimal feasible communication-conscious placement (which minimizes the total weighted Manhattan distance between the new module and existing demand points) can be computed with Θ(nlog n). Both resulting algorithms are practically easy to implement and show convincing experimental behavior. ACM Classification: C.3.e: Reconfigurable Hardware; F.2.2.c: Geometrical problems and computations

The facility location problem is a resource allocation problem that mainly deals with adequate placement of various types of facilities to serve a distributed set of demands satisfying the nature of interactions between the demands and facilities and optimizing the cost of placing the facilities and the quality of service.

bounds on the average distance from the

An n-town, n ∈ N, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form solution is known. We show that optimal n-towns can be computed in O(n 7.5) time. This is also practically useful, as it allows us to compute optimal solutions up to n = 80. Key words: Manhattan distance, average pairwise distance, integer points, dynamic programming 1.

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routing of multiple vehicles with no communications