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We revisit a classical load balancing problem in the modern context of decentralized systems and self-interested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client selfishly wants to minimize its own latency (job completion time). A server's latency is inversely proportional to its speed,(More)
We propose new algorithms and improved bounds for interference-aware routing in wireless networks. First, we prove that n arbitrarily matched source-destinations pairs with average distance d, for any 1 ≤ d ≤ √ n, in an O(n) size grid network achieve throughput capacity Ω(n/d). By a simple packing argument, this is also an upper bound in the worst-case. We(More)
We consider the problem of approximate range counting over streams of <i>d</i>-dimensional points. In the <i>data stream model</i>, the algorithm makes a single scan of the data, which is presented in an arbitrary order, and computes a compact summary (called a <i>sketch</i>). The sketch, whose size depends on the approximation parameter <i>&#949;</i>, can(More)
We propose a space-efficient scheme for summarizing multidimensional data streams. Our sketch can be used to solve spatial versions of several classical data stream queries efficiently. For instance, we can track ε-hotspots, which are congruent boxes containing at least an ε fraction of the stream, and maintain hierarchical heavy hitters in d dimensions.(More)
We generalize the notions of flippable and simultaneously flippable edges in a tri-angulation of a set S of points in the plane to so-called pseudo-simultaneously flippable edges. Such edges are related to the notion of convex decompositions spanned by S. We prove a worst-case tight lower bound for the number of pseudo-simultaneously flippable edges in a(More)
Heavy hitters, which are items occurring with frequency above a given threshold, are an important aggregation and summary tool when processing data streams or data warehouses. Hierarchical heavy hitters (HHHs) have been introduced as a natural generalization for hierarchical data domains, including multi-dimensional data. An item <i>x</i> in a hierarchy is(More)
Given n red and n blue points in the plane and a planar straight line matching between the red and the blue points, the matching can be extended into a bipartite planar straight line spanning tree. That is, any red-blue planar matching can be completed into a crossing-free red-blue spanning tree. Such a tree can be constructed in O(n log n) time.