Network Flows

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Some Recent Advances in Network Flows

The literature on network flow problems is extensive, and over the past 40 years researchers have made continuous improvements to algorithms for solving several classes of problems. However, the surge of activity on the algorithmic aspects of network flow problems over the past few years has been particularly striking. Several techniques have proven to be very successful in permitting researchers to make these recent contributions: (i) scaling of the problem data; (ii) improved analysis of algorithms, especially amortized average case performance and the use of potential functions; and (iii) enhanced data structures. In this survey, we illustrate some of these techniques and their usefulness in developing faster network flow algorithms. Our discussion focuses on the design of faster algorithms from the worst case perspective and we limit our discussion to the following fundamental problems: the shortest path problem, the maximum flow problem, and the minimum cost flow problem. We consider several representative algorithms from each problem class including the radix heap algorithm for the shortest path problem, preflow push algorithms for the maximum flow problem, and the pseudoflow push algorithms for the minimum cost flow problem

Algorithms for the simple equal flow problem

Includes bibliographical references (p. 30-32).HD28 .M414 no.3960-97,

Applications of network optimization

Includes bibliographical references (p. 41-48).HD28 .M414 no.3458-, 92,

Inverse optimization.

"(Revised January 27, 1998)"--T.p. -- "February 1998."--Cover.HD28 .M414 no.4002-98,

Inverse optimization.

"(Revised January 25, 1998)"--T.p. -- "February 1998."--Cover.HD28 .M414 no.4003-98,

A fast algorithm for the bipartite node weighted matching problmem on path graphics with application to the inverse spanning tree problem

"(Revised February 14, 1998.)"--T.p. -- "February 1998"--Cover.HD28 .M414 no.4006-98,

Use of representative operation counts in computational testings of algorithms

Includes bibliographical references (p. 25-26).HD28 .M414 no.3459-, 92,

Equivalence of primal and dual simplex algorithms for the maximum flow problem

HD28 .M414 no.3884-96,

New scaling algorithms for the assignment and minimum cycle mean problems

HD28 .M414 no.2019-, 88,