Shortest Cut Graph of a Surface with Prescribed Vertex Set
نویسنده
چکیده
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.
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