Path Minima Queries in Dynamic Weighted Trees

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


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.


Boundary Node Query Time Path Minimum Input Tree Lower Common Ancestor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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