Abstract.A set of n points in the plane is in equiangular configuration if there exist a center and an ordering of the points such that the angle of each two adjacent points w.r.t. the center is 360 • n , i.e., if all angles between adjacent points are equal. We show that there is at most one center of equiangularity, and we give a linear time algorithm that decides whether a given point set is in equiangular configuration, and if so, the algorithm outputs the center. A generalization of equiangularity is σ-angularity, where we are given a string σ of n angles and we ask for a center such that the sequence of angles between adjacent points is σ. We show that σ-angular configurations can be detected in time O(n 4 log n).
We propose SARP, a provably incentive-compatible and energy-efficient routing protocol for ad hoc networks. The key distinguishing factor when compared to previous proposals is the practicality and (relative) scalability of SARP due to a small communication complexity (analytically and practically), which is achieved by computing routing paths in a novel manner that borrows techniques from geometric routing. We also propose a solution on how to deliver payments (rather than only computing them). We support our claim that SARP works in realistic settings through comparative simulation results obtained from an implementation of SARP in GloMoSim.
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