
Connected max cut is polynomial for graphs without K_5 e as a minor
Given a graph G=(V, E), a connected cut δ (U) is the set of edges of E l...
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Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on co...
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An FFTbased method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid
We introduce an FFTbased solver for the combinatorial continuous maximu...
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CutToggling and CycleToggling for Electrical Flow and Other pNorm Flows
We study the problem of finding flows in undirected graphs so as to mini...
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Minimum 0Extension Problems on Directed Metrics
For a metric μ on a finite set T, the minimum 0extension problem 0Ext[...
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A Tight MaxFlow MinCut Duality Theorem for NonLinear Multicommodity Flows
The MaxFlow MinCut theorem is the classical duality result for the Max...
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Competitive Analysis of MinimumCut Maximum Flow Algorithms in Vision Problems
Rapid advances in image acquisition and storage technology underline the...
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Generalized maxflows and mincuts in simplicial complexes
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial (co)boundary operator we can state these problems as linear programs and show that they are dual to one another. Unlike graphs, complexes with integral capacity constraints may have fractional maxflows. We show that computing a maximum integral flow is NPhard. Moreover, we give a combinatorial definition of a simplicial cut that seems more natural in the context of optimization problems and show that computing such a cut is NPhard. However, we provide conditions on the simplicial complex for when the cut found by the linear program is a combinatorial cut. For ddimensional simplicial complexes embedded into ℝ^d+1 we provide algorithms operating on the dual graph: computing a maximum flow is dual to computing a shortest path and computing a minimum cut is dual to computing a minimum cost circulation. Finally, we investigate the FordFulkerson algorithm on simplicial complexes, prove its correctness, and provide a heuristic which guarantees it to halt.
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