Csaba D. Tóth

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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 present a multi-dimensional generalization of the Szemer&#233;di-Trotter Theorem, and give a sharp bound on the number of incidences of points and <i>not-too-degenerate</i> hyperplanes in three- or higher-dimensional Euclidean spaces. We call a hyperplane <i>not-too-degenerate</i> if at most a constant portion of its incident points lie in a lower(More)
We propose a low-overhead scheme for detecting a network partition or cut in a sensor network. Consider a network <i>S</i> of <i>n</i> sensors, modeled as points in a two-dimensional plane. An &epsiv;-<i>cut</i>, for any 0 &lt; &epsiv; &lt; 1, is a linear separation of &epsiv;<i>n</i> nodes in <i>S</i> from a distinguished node, the <i>base station</i>. Our(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 worstcase. 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)
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)
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-hot spots, which are congruent boxes containing at least an ε fraction of the stream, and maintain hierarchical heavy hitters in d dimensions.(More)
We study some geometric <?Pub Caret>maximization problems in theEuclidean plane under the non-crossing constraint. Given a set<?Pub Fmt italic>V<?Pub Fmt /italic> of<?Pub Fmt italic>2n<?Pub Fmt /italic> points in general position in theplane, we investigate the following geometric configurations usingstraight-line segments and the Euclidean norm: (i)(More)
It is shown that every disconnected vertex-colored plane straight line graph with no isolated vertices can be augmented (by adding edges) into a connected plane straight line graph such that the new edges respect the coloring and the degree of every vertex increases by at most two. The upper bound for the increase of vertex degrees is best possible: there(More)