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Given a directed graph with a capacity on each edge, the all-pairs bottleneck paths (APBP) problem is to determine , for all vertices s and t, the maximum flow that can be routed from s to t. For dense graphs this problem is equivalent to that of computing the (max, min)-transitive closure of a real-valued matrix. In this paper, we give a (max, min)-matrix(More)
We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities. Our algorithm views the allocation of money as flows and iteratively improves the balanced flow as in [Devanur et al. 2008] for Fisher's model. We develop new methods to carefully deal with the flows and(More)
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)
1 We construct an iterative algorithm for the solution of forward scattering problems in two dimensions. The scheme is based on the combination of high-order quadrature formulae, fast application of integral operators in Lippmann-Schwinger equations, and the stabilized biconjugate gradient method (BI-CGSTAB). While the FFT-based fast application of integral(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)