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Efficiency of the Network Simplex Algorithm for the Maximum Flow Problem.

Author: Andrew V Goldberg; Michael D Grigoriadis; Robert E Tarjan; PRINCETON UNIV NJ Dept. of COMPUTER SCIENCE.
Publisher: Ft. Belvoir : Defense Technical Information Center, OCT 1988.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
Goldfarb and Hao have proposed a network simplex algorithm that will solve a maximum flow problem on an n-vertex, m-arc network in at most nm pivots and O(n squared m) time. In this paper we describe how to implement their algorithm to run in O(nmlog n) time by using an extension of the dynamic tree data structure of Sleator and Tarjan. This bound is less than a logarithmic factor larger than that of any other known  Read more...
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Document Type: Book
All Authors / Contributors: Andrew V Goldberg; Michael D Grigoriadis; Robert E Tarjan; PRINCETON UNIV NJ Dept. of COMPUTER SCIENCE.
OCLC Number: 227751456
Description: 19 pages ; 23 x 29 cm

Abstract:

Goldfarb and Hao have proposed a network simplex algorithm that will solve a maximum flow problem on an n-vertex, m-arc network in at most nm pivots and O(n squared m) time. In this paper we describe how to implement their algorithm to run in O(nmlog n) time by using an extension of the dynamic tree data structure of Sleator and Tarjan. This bound is less than a logarithmic factor larger than that of any other known algorithm for the problem. Keywords: Algorithms; Complexity; Data structures; Dynamic trees; Graphs; Linear programming; Maximum flow; Network flow; Network optimization.

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