# ps9 - 6.889: Algorithms for Planar Graphs and Beyond...

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6.889: Algorithms for Planar Graphs and Beyond November 9, 2011 Problem Set 9 This problem set is due Wednesday, November 16 at noon. 1. Prove that the Steiner tree spanner as constructed in the lecture actually contains a Steiner tree of the given terminals of weight at most (1 + )OPT (where c is an absolute constant). Hint: Recall that the structure theorem guarantees that we can transform any forest inside a brick into another forest of slightly larger weight that includes E and W and that preserves connectivity among the boundary and has at most α joining vertices, where α = 2 c 0 κ± - 2 . 5 = O ( ± - 5 . 5 ). However, we do not know the joining vertices; hence we greedily selected θ = 2 α± - 1 · (MG) portals around each brick.
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## This note was uploaded on 01/20/2012 for the course CS 6.889 taught by Professor Erikdemaine during the Fall '11 term at MIT.

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