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Minimizing maximum flows in linear graphs
Author(s) -
Stanat D. F.,
Magó G. A.
Publication year - 1979
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230090405
Subject(s) - sink (geography) , minimax , maximum flow problem , graph , computer science , linear programming , flow network , mathematical optimization , combinatorics , mathematics , cartography , geography
We define a linear graph to be a connected acyclic graph each of whose nodes is of degree one or two. We consider a flow problem in linear graphs in which a commodity flows from source nodes to sink nodes. Each source node has a specified value denoting an amount of a commodity to be disposed of and each sink node has a specified capacity denoting the maximum amount of the commodity it can absorb; edges are capable of carrying an arbitrary quantity of the commodity. A solution is a set of flows which transports the commodity from all source nodes to sink nodes without overfilling any sink. A solution is defined to be optimal if it is minimax, that is, the largest flow along any edge is as small as possible. We describe 0(n 2 ) and 0(n) algorithms for finding optimal solutions.