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- Ran Duan, Seth Pettie
- SODA
- 2009

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)

The <i>maximum cardinality</i> and <i>maximum weight matching</i> problems can be solved in <i>Õ</i>(<i>m</i>√<i>n</i>) time, a bound that has resisted improvement despite decades of research. (Here <i>m</i> and <i>n</i> are the number of edges and vertices.) In this article, we demonstrate that this “<i>m</i>√<i>n</i>… (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)

- 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)

—Recent development of sophisticated smartphones has made them indispensable part of our everyday life. However, advances in battery technology cannot keep up with the demand for longer battery life. Subsequently, energy efficiency has become one of the most important factors in designing smartphones. Multitasking and better multimedia features in the… (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)

- Ran Duan, Seth Pettie
- SODA
- 2009

Spontaneous failure is an unavoidable aspect of all networks , particularly those with a physical basis such as communications networks or road networks. Whether due to malicious coordinated attacks or other causes, failures temporarily change the topology of the network and, as a consequence, its connectivity and distance metric. In this paper we look at… (More)

- Ran Duan, Seth Pettie
- FOCS
- 2010

—Given a weighted graph, the maximum weight matching problem (MWM) is to find a set of vertex-disjoint edges with maximum weight. In the 1960s Edmonds showed that MWMs can be found in polynomial time. At present the fastest MWM algorithm, due to Gabow and Tarjan, runs iñ O(m √ n) time, where m and n are the number of edges and vertices in the graph.… (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)