Abstract. Given n demand points in the plane, the p-center problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo& point to its respective nearest supply point. The p-median problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the p-center and the p-media problems relative to both the Euclidean and the rectilinear metrics are NP-hard. In fact, we prove that it is NP-hard even to approximate the p-center problems sufficiently closely. The reductions are from 3-satisfiability.
The ordered binary decision diagram is a canonical representation for Boolean functions, presented by Bryant as a compact representation for a broad class of interesting functions derived from circuits. However, the size of the diagram is very sensitive to the choice of ordering on the variables; hence for some applications, such as Differential Cascade Voltage Switch (DCVS) trees, it becomes extremely important to find the ordering leading to the most compact representation. We present an algorithm for this problem with time complexity C(n23"), an improvement over the previous best, which required G(n!2").
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