208 research outputs found

    A Decomposition Algorithm for Nested Resource Allocation Problems

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    We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict convexity or differentiability is needed. The method solves a hierarchy of resource allocation subproblems, whose solutions are used to convert constraints on sums of resources into bounds for separate variables at higher levels. The resulting time complexity for the integer problem is O(nlogmlog(B/n))O(n \log m \log (B/n)), and the complexity of obtaining an ϵ\epsilon-approximate solution for the continuous case is O(nlogmlog(B/ϵ))O(n \log m \log (B/\epsilon)), nn being the number of variables, mm the number of ascending constraints (such that m<nm < n), ϵ\epsilon a desired precision, and BB the total resource. This algorithm attains the best-known complexity when m=nm = n, and improves it when logm=o(logn)\log m = o(\log n). Extensive experimental analyses are conducted with four recent algorithms on various continuous problems issued from theory and practice. The proposed method achieves a higher performance than previous algorithms, addressing all problems with up to one million variables in less than one minute on a modern computer.Comment: Working Paper -- MIT, 23 page

    Implications of Selfish Neighbor Selection in Overlay Networks

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    In a typical overlay network for routing or content sharing, each node must select a fixed number of immediate overlay neighbors for routing traffic or content queries. A selfish node entering such a network would select neighbors so as to minimize the weighted sum of expected access costs to all its destinations. Previous work on selfish neighbor selection has built intuition with simple models where edges are undirected, access costs are modeled by hop-counts, and nodes have potentially unbounded degrees. However, in practice, important constraints not captured by these models lead to richer games with substantively and fundamentally different outcomes. Our work models neighbor selection as a game involving directed links, constraints on the number of allowed neighbors, and costs reflecting both network latency and node preference. We express a node's "best response" wiring strategy as a k-median problem on asymmetric distance, and use this formulation to obtain pure Nash equilibria. We experimentally examine the properties of such stable wirings on synthetic topologies, as well as on real topologies and maps constructed from PlanetLab and AS-level Internet measurements. Our results indicate that selfish nodes can reap substantial performance benefits when connecting to overlay networks composed of non-selfish nodes. On the other hand, in overlays that are dominated by selfish nodes, the resulting stable wirings are optimized to such great extent that even non-selfish newcomers can extract near-optimal performance through naive wiring strategies.Marie Curie Outgoing International Fellowship of the EU (MOIF-CT-2005-007230); National Science Foundation (CNS Cybertrust 0524477, CNS NeTS 0520166, CNS ITR 0205294, EIA RI 020206
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