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A simple Newton-like descent algorithm for linear programming is proposed together with results of preliminary computational experiments on small- and medium-size problems. The proposed algorithm gives local superlinear convergence to the optimum and, experimentally, shows global linear convergence. It is similar to Karmarkar's algorithm in that it is an(More)
This paper presents an approach, called the ``topology-oriented approach,'' to numerically robust geometric algorithms. In this approach, the basic part of the algorithm is described in terms of combinatorial and topological computation primarily; this description guarantees robustness of the algorithm because combinatorial and topological computation is(More)
We extend the concept of Voronoi diagram in the ordinary Euclidean geometry for n points to the one in the Laguerre geometry for n circles in the plane, where the distance between a circle and a point is defined by the length of the tangent line, and show that there is an O(n log n) algorithm for this extended case. The Voronoi diagram in the Laguerre(More)
The cost–scaling algorithm of Goldberg and Tarjan [9] is known to be one of the most efficient algorithms for minimum–cost flow problems. However, its efficiency in practice depends on many implementation aspects. Moreover, the inclusion of several heuristics improves its performance drastically. This paper addresses important implementation aspects and(More)
Several linear-time approximation algorithms for the minimum-weight perfect matching in a plane are proposed, and their worstand average-case behaviors are analyzed theoretically as well as experimentally. A linear-time approximation algorithm, named the “spiral-rack algorithm (with preprocess and with tour),” is recommended for practical purposes. This(More)