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Mathematical Programming

, Volume 78, Issue 2, pp 169–177 | Cite as

Dynamic trees as search trees via euler tours, applied to the network simplex algorithm

  • Robert E. Tarjan
Article

Abstract

Thedynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges (linking) and splitting by deleting edges (cutting), while at the same time allowing reporting of certain combinations of vertex or edge values. For many applications of dynamic trees, values must be combined along paths. For other applications, values must be combined over entire trees. For the latter situation, an idea used originally in parallel graph algorithms, to represent trees by Euler tours, leads to a simple implementation with a time of O(logn) per tree operation, wheren is the number of tree vertices. We apply this representation to the implementation of two versions of the network simplex algorithm, resulting in a time of O(logn) per pivot, wheren is the number of vertices in the problem network.

Keywords

Search Tree Tree Operation Dynamic Tree Minimum Cost Flow Euler Tour 
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

© The Mathematical Programming Society, Inc 1997

Authors and Affiliations

  • Robert E. Tarjan
    • 1
    • 2
  1. 1.Department of Computer SciencePrinceton UniversityPrinceton
  2. 2.NEC Research InstitutePrincetonUSA

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