Finding small simple cycle separators for 2-connected planar graphs
Journal of Computer and System Sciences
Parallel algorithms for minimum cuts and maximum flows in planar networks
Journal of the ACM (JACM)
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
A new approach to the maximum-flow 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
A deterministic near-linear time algorithm for finding minimum cuts in planar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Computing the Girth of a Planar Graph in $O(n \logn)$ Time
SIAM Journal on Discrete Mathematics
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Computing the girth of a planar graph in linear time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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
Min-cuts and shortest cycles in planar graphs in O(n log log n) time
ESA'11 Proceedings of the 19th European conference on Algorithms
Submatrix maximum queries in Monge matrices and Monge partial matrices, and their applications
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Annotating simplices with a homology basis and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Structured recursive separator decompositions for planar graphs in linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Linear-time algorithms for max flow and multiple-source shortest paths in unit-weight planar graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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We study the min st-cut and max st-flow problems in planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph and two vertices s and t computes a min st-cut in O(n log log n) time. Second, we show how to achieve the same bound for the problem of computing a max st-flow in an undirected planar graph. These are the first algorithms breaking the O(n log n) barrier for those two problems, which has been standing for more than 25 years. Third, we present a fully dynamic algorithm maintaining the value of the min st-cuts and the max st-flows in an undirected plane graph (i.e., a planar graph with a fixed embedding): our algorithm is able to insert and delete edges and answer queries for min st-cut/max st-flow values between any pair of vertices s and t in O(n(2/3) log(8/3) n) time per operation. This result is based on a new dynamic shortest path algorithm for planar graphs which may be of independent interest. We remark that this is the first known non-trivial dynamic algorithm for min st-cut and max st-flow.