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We show how auction algorithms, originally developed for the assignment problem, can be utilized in Merriman, Bence, and Osher's threshold dynamics scheme to simulate multi-phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases. The resulting algorithms are highly efficient and robust, and can be used in simulations ranging from minimal partition problems in Euclidean space to semi-supervised machine learning via clustering on graphs. In the case of the latter application, numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state-of-the-art methods, while requiring a fraction of the computation time. [ABSTRACT FROM AUTHOR]

Abstract: We consider the following model of cellular networks. Each base station has a given finite capacity, and each client has some demand and profit. A client can be covered by a specific subset of the base stations, and its profit is obtained only if its demand is provided in full. The goal is to assign clients to base stations, so that the overall profit is maximized subject to base station capacity constraints. In this work, we present a distributed algorithm for the problem, that runs in polylogarithmic time, and guarantees an approximation ratio close to the best known ratio achievable by a centralized algorithm. [Copyright &y& Elsevier]

Abstract: We study an aggregation problem in which a society has to determine its position on each of several issues, based on the positions of the members of the society on those issues. There is a prescribed set of feasible evaluations, i.e., permissible combinations of positions on the issues. The binary case of this problem, where only two positions are allowed on each issue, is by now quite well understood. We consider arbitrary sets of conceivable positions on each issue. This general framework admits the modeling of aggregation of various types of evaluations, including: assignments of candidates to jobs, choice functions from sets of alternatives, judgments in many-valued logic, probability estimates for events, etc. We require that the aggregation be performed issue-by-issue, and that the social position on each issue be supported by at least one member of the society. The set of feasible evaluations is called an impossibility domain if these requirements are satisfied for it only by dictatorial aggregation; that is to say, if it gives rise to an analogue of Arrow''s impossibility theorem for preference aggregation. We obtain a two-part sufficient condition for an impossibility domain, and show that the major part is a necessary condition. For the ternary case, where three positions are allowed on each issue, we get a full characterization of impossibility domains. [Copyright &y& Elsevier]