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CORR
2012
Springer

Multiple-Source Shortest Paths in Embedded Graphs

8 years 5 months ago
Multiple-Source Shortest Paths in Embedded Graphs
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe an algorithm to preprocess the graph in O(gnlog n) time, so that the shortest-path distance from any vertex on the boundary of f to any other vertex in G can be retrieved in O(log n) time. Our result directly generalizes the O(nlog n)-time algorithm of Klein [Multiple-source shortest paths in planar graphs. In Proc. 16th Ann. ACM-SIAM Symp. Discrete Algorithms, 2005] for multiple-source shortest paths in planar graphs. Intuitively, our preprocessing algorithm maintains a shortest-path tree as its source point moves continuously around the boundary of f . As an application of our algorithm, we describe algorithms to compute a shortest non-contractible or non-separating cycle in embedded, undirected graphs in O(g2 nlog n) time.
Sergio Cabello, Erin W. Chambers, Jeff Erickson
Added 20 Apr 2012
Updated 20 Apr 2012
Type Journal
Year 2012
Where CORR
Authors Sergio Cabello, Erin W. Chambers, Jeff Erickson
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