Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Introduction to Algorithms
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth 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
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
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
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
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We describe a simple greedy algorithm whose input is a set P of vertices on a combinatorial surface S without boundary and that computes a shortest cut graph of S with vertex set P. (A cut graph is an embedded graph whose removal leaves a single topological disk.) If S has genus g and complexity n, the running-time is O(n log n+(g + |P|)n). This is an extension of an algorithm by Erickson and Whittlesey [Proc. ACM-SIAM Symp. on Discrete Algorithms, 1038-1046 (2005)], which computes a shortest cut graph with a single given vertex. Moreover, our proof is simpler and also reveals that the algorithm actually computes a minimum-weight basis of some matroid.