STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Escaping a grid by edge-disjoint paths
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Efficient Algorithms for k-Terminal Cuts on Planar Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
The combinatorial approach yields an NC algorithm for computing Pfaffians
Discrete Applied Mathematics
Processor efficient parallel matching
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
An O (n log n) algorithm for maximum st-flow in a directed planar graph
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An O(n log n) algorithm for maximum st-flow in a directed planar graph
Journal of the ACM (JACM)
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Computing Large Matchings in Planar Graphs with Fixed Minimum Degree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
ACM Transactions on Algorithms (TALG)
Network flow interdiction on planar graphs
Discrete Applied Mathematics
Computing large matchings fast
ACM Transactions on Algorithms (TALG)
Maximum flows and parametric shortest paths in planar graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Computing large matchings in planar graphs with fixed minimum degree
Theoretical Computer Science
On the Power of Isolation in Planar Graphs
ACM Transactions on Computation Theory (TOCT)
Multiple-source single-sink maximum flow in directed planar graphs in O(diameter ċ n log n) time
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A new NC-algorithm for finding a perfect matching in d-regular bipartite graphs when d is small
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Inner rectangular drawings of plane graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Space complexity of perfect matching in bounded genus bipartite graphs
Journal of Computer and System Sciences
GD'11 Proceedings of the 19th international conference on Graph Drawing
Planarizing gadgets for perfect matching do not exist
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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The problem of maximum flow in planar graphs has always been investigated under the assumption that there is only one source and one sink. Here we consider the case where there are many sources and sinks (single commodity) in a directed planar graph. An algorithm for the case when the demands of the sources and sinks are fixed and given in advance is presented. It can be implemented efficiently sequentially and in parallel and its complexity is dominated by the complexity of computing all shortest paths from a single source in a planar graph. If the demands are not known, an algorithm for computing the maximum flow is presented for the case where the number of faces that contain sources and sinks is bounded by a slowly growing function. Our result places the problem of computing a perfect matching in a planar bipartite graph in NC and it improves a previous parallel algorithm for the case of a single source, single sink in a planar directed1nd undirected) graph, both in terms of processor bounds and in its simple presentation.