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Subway Network Algorithm Matt Freeburg ICS 311 Fall 2006 University of Hawaii at Manoa

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Table of Contents Introduction Introduction Correctness Correctness Algorithm Algorithm Complexity Complexity Conclusions Conclusions

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Consider Vertex v, a child of t, with children ui, i from 1 to n Vertex v, a child of t, with children ui, i from 1 to n P(v) = p P(v) = p Each child is a subtree that requires ki machines to clean Each child is a subtree that requires ki machines to clean We order ui so ki are in decreasing order, without loss of generality We order ui so ki are in decreasing order, without loss of generality

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Lemma 1 When cleaning subtrees ui from i = 1 to n, number of machines needed is K, such that k1