Data structures and network algorithms
Data structures and network algorithms
Making data structures persistent
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Matching is as easy as matrix inversion
Combinatorica
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Splitting (complicated) surfaces is hard
Proceedings of the twenty-second annual symposium on Computational geometry
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
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Finding shortest contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
Output-sensitive algorithm for the edge-width of an embedded graph
Proceedings of the twenty-sixth annual symposium on Computational geometry
Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
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
The tight orthogonal homotopic bases of closed oriented triangulated surfaces and their computing
Computers & Mathematics with Applications
Improved algorithms for min cut and max flow in undirected planar graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On graph crossing number and edge planarization
Proceedings of the twenty-second 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
Computing replacement paths in surface embedded graphs
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
From the plane to higher surfaces
Journal of Combinatorial Theory Series B
Finding Cycles with Topological Properties in Embedded Graphs
SIAM Journal on Discrete Mathematics
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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
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We give an O(g2nlog n) algorithm to represent the shortest path tree from all the vertices on a single specified face f in a genus g graph. From this representation, any query distance from a vertex in f can be obtained in O(log n) time. The algorithm uses a kinetic data structure, where the source of the tree iteratively moves across edges in f. In addition, we give applications using these shortest path trees in order to compute the shortest non-contractible cycle and the shortest non-separating cycle embedded on an orientable 2-manifold in O(g3nlog n) time.