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The Lovasz Local Lemma (LLL), introduced by Erdos and Lovasz in 1975, is a powerful tool of the probabilistic method that allows one to prove that a set of n "bad" events do not happen with non-zero probability, provided that the events have limited dependence. However, the LLL itself does not suggest how to find a point avoiding all bad events. Since the(More)
The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier” is extremely fragile, in the following sense. For any > 0, we give an algorithm that(More)
Given a tree T with weight and length on each edge, as well as a lower bound L and an upper bound U , the so-called length-constrained maximum-density subtree problem is to find a maximum-density subtree in T such that the length of this subtree is between L and U . In this study, we present an algorithm that runs in O(nU log n) time for the case when the(More)
We study the problem of computing the minimum cut in a weighted distributed messagepassing networks (the CONGEST model). Let λ be the minimum cut, n be the number of nodes (processors) in the network, and D be the network diameter. Our algorithm can compute λ exactly in O(( √ n log∗ n+D)λ log n) time. To the best of our knowledge, this is the first paper(More)
Graph coloring is a central problem in distributed computing. Both vertexand edge-coloring problems have been extensively studied in this context. In this paper we show that a (2∆ − 1)-edge-coloring can be computed in time smaller than log n for any > 0, specifically, in e √ log logn) rounds. This establishes a separation between the (2∆ − 1)-edge-coloring(More)