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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; Stanford University. Computer Science Department.
Publisher: Stanford, Calif. : Dept. of Computer Science, Stanford University, 1989.
Series: Report (Stanford University. Computer Science Department), no. STAN-CS-89-1248.
Edition/Format:   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(n2m) time. In this paper we describe how to implement their algorithm to run in O(nm log 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; Stanford University. Computer Science Department.
OCLC Number: 20257481
Notes: "February 1989."
Description: 17 pages : illustrations ; 28 cm.
Series Title: Report (Stanford University. Computer Science Department), no. STAN-CS-89-1248.
Responsibility: Andrew V. Goldberg, Michael D. Grigoriadis, Robert E. Tarjan.

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(n2m) time. In this paper we describe how to implement their algorithm to run in O(nm log 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.

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