A New approach in the maximum flow problem
Author(s)
Advisor
Akgül, MustafaDate
1989Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
197
views
views
114
downloads
downloads
Abstract
In this study, we tried to approach the maximum flow
problem from a different point of view. This effort has
led us to the development of a new maximum flow algorithm.
The algorithm is based on the idea that when initial
quasi-flow on each edge of the graph is equated to the upper
capacity of the edge, it violates node balance equations,
while satisfying capacity and non-negativity constraints.
In order to obtain a feasible and optimum flow, quasi-flow
on some of the edges have to be reduced. Given an initial
quasi-flow, positive and negative excess, and, balanced
nodes are determined. Algorithm reduces excesses of
unbalanced nodes to zero by finding residual paths joining
positive excess nodes to negative excess nodes and sending
excesses along these paths. Minimum cut is determined
first, and then maximum flow of the given cut is found.
Time complexity of the algorithm is o(n^m). The application
of the modified version of the Dynamic Tree structure of
Sleator and Tarjan reduces it to o(nmlogn).