Path Minima Queries in Dynamic Weighted Trees

  • Gerth Stølting Brodal
  • Pooya Davoodi
  • S. Srinivasa Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

Abstract

In the path minima problem on trees each tree edge is assigned a weight and a query asks for the edge with minimum weight on a path between two nodes. For the dynamic version of the problem on a tree, where the edge-weights can be updated, we give comparison-based and RAM data structures that achieve optimal query time. These structures support inserting a node on an edge, inserting a leaf, and contracting edges. When only insertion and deletion of leaves in a tree are needed, we give two data structures that achieve optimal and significantly lower query times than when updating the edge-weights is allowed. One is a semigroup structure for which the edge-weights are from an arbitrary semigroup and queries ask for the semigroup-sum of the edge-weights on a given path. For the other structure the edge-weights are given in the word RAM. We complement these upper bounds with lower bounds for different variants of the problem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Pooya Davoodi
    • 1
  • S. Srinivasa Rao
    • 2
  1. 1.MADALGO, Department of Computer ScienceAarhus UniversityDenmark
  2. 2.School of Computer Science and EngineeringSeoul National UniversitySouth Korea

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