Abstract
Let T be a tree on a set V of nodes. The p-th power T p of T is the graph on V such that any two nodes u and w of V are adjacent in T p if and only if the distance of u and w in T is at most p. Given an n-node m-edge graph G and a positive integer p, the p-th tree root problem asks for a tree T, if any, such that G=T p. Given a graph G, the tree root problem asks for a positive integer p and a tree T, if any, such that G=T p. Kearney and Corneil gave the best previously known algorithms for both problems. Their algorithm for the former (respectively, latter) problem runs in O(n 3) (respectively, O(n 4)) time. In this paper, we give O(n+m)-time algorithms for both problems.
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© 2006 Springer-Verlag Berlin Heidelberg
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Chang, MS., Ko, MT., Lu, HI. (2006). Linear-Time Algorithms for Tree Root Problems. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_38
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DOI: https://doi.org/10.1007/11785293_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35753-7
Online ISBN: 978-3-540-35755-1
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