6.889: Algorithms for Planar Graphs and Beyond (Fall 2011)

Erik Demaine, Shay Mozes, Christian Sommer, Siamak Tazari

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[+] Multiple-source shortest paths.

Based on interdigitating trees from Lecture 2 (they're ubiquitous!) and dynamic trees, we discuss how to efficiently transform a shortest-path tree rooted at r into an SP tree rooted at its neighbor r', and then on to r'', for all the nodes on any face of a planar graph. We shall see that, by doing so, we can compute the shortest-path distance from all the nodes on a single face in time O(n log n) (plus roughly the number of distances output).

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Lecture notes, page 1/6 • [previous page] • [next page] • [PDF]

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