A B S T R A C TWe present an algorithm for determining the shortest path between a source point and any destination point along the surface of a polyhedron (need not be convex).Our algorithm uses a new approach which deviates from the conventional "continuous Dijkstra" technique. It takes O(n 2) time and O(n) space to determine the shortest path and to compute the inward layout which can be used to construct a structure for processing queries of shortest path from the source point to any destination point.

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We present an algorithm for determining the shortest path between any two points along the surface of a polyhedron which need not be convex. This algorithm also computes for any source point on the surface of a polyhedron the inward layout and the subdivision of the polyhedron which can be used for processing queries of shortest paths between the source point and any destination point. Our algorithm uses a new approach which deviates from the conventional “continuous Dijkstra” technique. Our algorithm has time complexity O(n2) and space complexity Θ(n).

Abstract-Broadcast is a fundamental operation in wireless networks, and naïve flooding is not practical, because it cannot deal with interference. Scheduling is a good way of avoiding interference, but previous studies on broadcast scheduling algorithms all assume highly theoretical models such as the unit disk graph model. In this work, we reinvestigate this problem by using the 2-Disk and the signal-to-interference-plus-noise-ratio (SINR) models. We first design a constant approximation algorithm for the 2-Disk model and then extend it to the SINR model. This result, to the best of our knowledge, is the first result on broadcast scheduling algorithms in the SINR model.

This paper resolves a long-standing open problem on whether the concurrent write capability of parallel random access machine (PRAM) is essential for solving fundamental graph problems like connected components and minimum spanning trees in O (log n ) time. Specifically, we present a new algorithm to solve these problems in O (log n ) time using a linear number of processors on the exclusive-read exclusive-write PRAM. The logarithmic time bound is actually optimal since it is well known that even computing the “OR” of n bit requires Ω(log n time on the exclusive-write PRAM. The efficiency achieved by the new algorithm is based on a new schedule which can exploit a high degree of parallelism.

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We present an O(n 3 (log log n/ log n) 5/4 ) time algorithm for all pairs shortest paths. This algorithm improves on the best previous result of O(n 3 / log n) time.