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- Ran Duan, Hsin-Hao Su
- SODA
- 2012

Given a weighted bipartite graph, the maximum weight matching (MWM) problem is to find a set of vertex-disjoint edges with maximum weight. We present a new scaling algorithm that runs in O(m √ n log N) time, when the weights are integers within the range of [0, N ]. The result improves the previous bounds of O(N m √ n) by Gabow and O(m √ n log (nN)) by… (More)

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˜O(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)

Graph coloring is a central problem in distributed computing. Both vertex-and 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 O(√ log log n) rounds. This establishes a separation between the (2∆ −… (More)

a r t i c l e i n f o a b s t r a c t 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… (More)

In this paper, we study the problems of enumerating cuts of a graph by non-decreasing weights. There are four problems, depending on whether the graph is directed or undirected, and on whether we consider all cuts of the graph or only s-t cuts for a given pair of vertices s, t. Efficient algorithms for these problems with˜O(n 2 m) delay between two… (More)

Vertex coloring is a central concept in graph theory and an important symmetry-breaking primitive in distributed computing. Whereas degree-∆ graphs may require palettes of ∆+1 colors in the worst case, it is well known that the chromatic number of many natural graph classes can be much smaller. In this paper we give new distributed algorithms to find… (More)

Vertex coloring is a central concept in graph theory and an important symmetry-breaking primitive in distributed computing. Whereas degree-∆ graphs may require palettes of ∆ + 1 colors in the worst case, it is well known that the chromatic number of many natural graph classes can be much smaller. In this paper we give new distributed algorithms to find… (More)

The (∆+1)-coloring problem is a fundamental symmetry breaking problem in distributed computing. We give a new randomized coloring algorithm for (∆+1)-coloring running in O(√log ∆)+ 2^O(√log log n) rounds with probability 1-1/n^Ω(1) in a graph with n nodes and maximum degree ∆. This implies that the… (More)

We study the problem of computing the minimum cut in a weighted distributed message-passing 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 4 log 2 n) time. To the best of our knowledge, this is the first… (More)