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34
An Experimental Comparison of MinCut/MaxFlow Algorithms for Energy Minimization in Vision
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time compl ..."
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Cited by 794 (48 self)
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After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper
Faster ShortestPath Algorithms for Planar Graphs
 STOC 94
, 1994
"... We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required\O ..."
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Cited by 167 (14 self)
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We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required\Omega\Gamma n p log n) time where n is the number of nodes in the input graph. For the case where negative edgelengths are allowed, we give an algorithm requiring O(n 4=3 log nL) time, where L is the absolute value of the most negative length. Previous algorithms for shortest paths with negative edgelengths required \Omega\Gamma n 3=2 ) time. Our shortestpath algorithm yields an O(n 4=3 log n)time algorithm for finding a perfect matching in a planar bipartite graph. A similar improvement is obtained for maximum flow in a directed planar graph.
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time
 In Proc. 42nd IEEE Annual Symposium on Foundations of Computer Science
, 2001
"... for finding shortest paths in a planar graph with real weights. ..."
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Cited by 54 (0 self)
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for finding shortest paths in a planar graph with real weights.
An O(n log n) algorithm for maximum stflow in a directed planar graph
"... We give the first correct O(n log n) algorithm for finding a maximum stflow in a directed planar graph. After a preprocessing step that consists in finding singlesource shortestpath distances in the dual, the algorithm consists of repeatedly saturating the leftmost residual stot path. ..."
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Cited by 28 (0 self)
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We give the first correct O(n log n) algorithm for finding a maximum stflow in a directed planar graph. After a preprocessing step that consists in finding singlesource shortestpath distances in the dual, the algorithm consists of repeatedly saturating the leftmost residual stot path.
Shortest paths in directed planar graphs with negative lengths: A linearspace O(n log² n)time algorithm
 PROC. 20TH ANN. ACMSIAM SYMP. DISCRETE ALGORITHMS
, 2009
"... We give an O(n log² n)time, linearspace algorithm that, given a directed planar graph with positive and negative arclengths, and given a node s, finds the distances from s to all nodes. ..."
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Cited by 21 (5 self)
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We give an O(n log² n)time, linearspace algorithm that, given a directed planar graph with positive and negative arclengths, and given a node s, finds the distances from s to all nodes.
Minimum Cuts and Shortest Homologous Cycles
 SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2009
"... We describe the first algorithms to compute minimum cuts in surfaceembedded graphs in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s, t)cut in g O(g) n log n time. Except for the spec ..."
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Cited by 20 (7 self)
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We describe the first algorithms to compute minimum cuts in surfaceembedded graphs in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s, t)cut in g O(g) n log n time. Except for the special case of planar graphs, for which O(n log n)time algorithms have been known for more than 20 years, the best previous time bounds for finding minimum cuts in embedded graphs follow from algorithms for general sparse graphs. A slight generalization of our minimumcut algorithm computes a minimumcost subgraph in every Z2homology class. We also prove that finding a minimumcost subgraph homologous to a single input cycle is NPhard.
Maximum matchings in planar graphs via Gaussian elimination
 ALGORITHMICA
, 2004
"... We present a randomized algorithm for finding maximum matchings in planar graphs in time O(n ω/2), where ω is the exponent of the best known matrix multiplication algorithm. Since ω < 2.38, this algorithm breaks through the O(n 1.5) barrier for the matching problem. This is the first result of this ..."
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Cited by 16 (2 self)
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We present a randomized algorithm for finding maximum matchings in planar graphs in time O(n ω/2), where ω is the exponent of the best known matrix multiplication algorithm. Since ω < 2.38, this algorithm breaks through the O(n 1.5) barrier for the matching problem. This is the first result of this kind for general planar graphs. We also present an algorithm for generating perfect matchings in planar graphs uniformly at random using O(n ω/2) arithmetic operations. Our algorithms are based on the Gaussian elimination approach to maximum matchings introduced in [1].
Homology flows, cohomology cuts
 ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2009
"... We describe the first algorithms to compute maximum flows in surfaceembedded graphs in nearlinear time. Specifically, given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, we can compute a maximum (s, t)flow in O(g 7 n log 2 n log 2 C) time fo ..."
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Cited by 16 (6 self)
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We describe the first algorithms to compute maximum flows in surfaceembedded graphs in nearlinear time. Specifically, given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, we can compute a maximum (s, t)flow in O(g 7 n log 2 n log 2 C) time for integer capacities that sum to C, or in (g log n) O(g) n time for real capacities. Except for the special case of planar graphs, for which an O(n log n)time algorithm has been known for 20 years, the best previous time bounds for maximum flows in surfaceembedded graphs follow from algorithms for general sparse graphs. Our key insight is to optimize the relative homology class of the flow, rather than directly optimizing the flow itself. A dual formulation of our algorithm computes the minimumcost cycle or circulation in a given (real or integer) homology class.
Improved Algorithms for Dynamic Shortest Paths
 Algorithmica
, 1996
"... We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can ..."
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Cited by 15 (3 self)
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We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time and a distance query is answered also in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to nvertex digraphs of genus O(n 1\Gamma" ) for any " ? 0. Keywords: Shortest path, dynamic algorithm, planar digraph, outerplanar digraph. This work was partially supported by the NSF grant No. CCR9409191 and by the EU ESPRIT LTR Project No. 20244 (ALCOMIT). 1 Introduction 1.1 The prob...