Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Randomized algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
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 partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
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
ACM Transactions on Algorithms (TALG)
Computing the Shortest Essential Cycle
Discrete & Computational Geometry
Maximum flows and parametric shortest paths in planar graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shortest vertex-disjoint two-face paths in planar graphs
ACM Transactions on Algorithms (TALG)
Shortest cut graph of a surface with prescribed vertex set
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Algorithms for the edge-width of an embedded graph
Computational Geometry: Theory and Applications
Finding Cycles with Topological Properties in Embedded Graphs
SIAM Journal on Discrete Mathematics
The complexity of separating points in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Let D be a weighted directed graph cellularly embedded in a surface of genus g, orientable or not, possibly with boundary. We describe algorithms to compute a shortest non-contractible and a shortest surface non-separating cycle in D. This generalizes previous results that only dealt with undirected graphs. Our first algorithm computes such cycles in O(n2 log n) time, where n is the total number of vertices and edges of D, thus matching the complexity of the best known algorithm in the undirected case. It revisits and extends Thomassen's 3-path condition; the technique applies to other families of cycles as well. We also give an algorithm with subquadratic complexity in the complexity of the input graph, if g is fixed. Specifically, we can solve the problem in O(√g n3/2 log n) time, using a divide-and-conquer technique that simplifies the graph while preserving the topological properties of its cycles. A variant runs in O(ng log g + n log2 n) for graphs of bounded treewidth.