Path minima in incremental unrooted trees

Haim Kaplan*, Nira Shafrir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Consider a dynamic forest of unrooted trees over a set of n vertices which we update by link operations: Each link operation adds a new edge adjacent to vertices in two different trees. Every edge in the forest has a weight associated with it, and at any time we want to be able to answer a path-min query which returns that edge of minimum weight along the path between two given vertices. For the case where the weights are integers we give an algorithm that performs n∈-∈1 link operations and m pathmin queries in O(n + mα(m,n)) time. This extends well known results of Tarjan [11] and Yao [12] to a more general dynamic setting at the cost of restricting the weights to be integers. We also suggest a simpler data structures for the case where trees are rooted and the link operation always adds an edge between the root of one tree and an arbitrary vertex of another tree.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2008 - 16th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540877436, 9783540877431
StatePublished - 2008
Event16th Annual European Symposium on Algorithms, ESA 2008 - Karlsruhe, Germany
Duration: 15 Sep 200817 Sep 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5193 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th Annual European Symposium on Algorithms, ESA 2008


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