Journal of the ACM (JACM)
A new approach to the minimum cut problem
Journal of the ACM (JACM)
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Maximum (s,t)-flows in planar networks in O(|V| log |V|) time
Journal of Computer and System Sciences
Minimum cuts in near-linear time
Journal of the ACM (JACM)
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Computing the Girth of a Planar Graph in O(n logn) Time
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ACM Transactions on Algorithms (TALG)
A faster algorithm for computing the girth of planar and bounded genus graphs
ACM Transactions on Algorithms (TALG)
Computing the Girth of a Planar Graph in $O(n \logn)$ Time
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Computing the girth of a planar graph in linear time
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Min-cuts and shortest cycles in planar graphs in O(n log log n) time
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Global minimum cuts in surface embedded graphs
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Discrete Optimization
A fast algorithm for minimum weight odd circuits and cuts in planar graphs
Operations Research Letters
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present a simple deterministic O(n log2 n)-time divide-and-conquer algorithm for finding minimum cuts in planar graphs. This can be compared to a randomized algorithm for general graphs by Karger that runs in time O(m log3 n) and also a deterministic algorithm for general graphs by Nagamochi and Ibaraki that runs in time O(mn + n2 log n). We use shortest paths in the dual graphs to partition the problem, and use the relationship between minimum cuts in primal graphs and shortest paths in dual graphs to find minimum cuts that cross the partitions efficiently.