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

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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.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, 08544, Princeton, NJ

    Robert E. Tarjan

  2. NEC Research Institute, 4 Independence Way, 08540, Princeton, NJ, USA

    Robert E. Tarjan

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  1. Robert E. Tarjan
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Additional information

Research at Princeton University partially supported by the National Science Foundation, Grant No. CCR-8920505, and the Office of Naval Research, Contract No. N0014-91-J-1463. Work during a visit to M.I.T. partially supported by ARPA Contract No. 14-95-1-1246.

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Tarjan, R.E. Dynamic trees as search trees via euler tours, applied to the network simplex algorithm. Mathematical Programming 78, 169–177 (1997). https://doi.org/10.1007/BF02614369

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  • DOI: https://doi.org/10.1007/BF02614369

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