6.889: Algorithms for Planar Graphs and Beyond (Fall 2011)
[Problem Session Notes]
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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