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Note on independence of arcs in antiparallel for network flow problems
Author(s) -
Hagstrom Jane Nichols
Publication year - 1984
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.3230140407
Subject(s) - antiparallel (mathematics) , independence (probability theory) , flow network , flow (mathematics) , mathematics , arc (geometry) , combinatorics , mathematical optimization , statistics , geometry , physics , quantum mechanics , magnetic field
Given a transportation flow network with two arcs in antiparallel, if the capacities of all other arcs are fixed and the demands at sinks are fixed, at least one of the two arcs will be irrelevant to the problem of flow feasibility. As a consequence, in a stochastic setting, two arcs in antiparallel whose capacities are independent of other network capacities and demands may be treated as having independent probability distributions regardless of their actual correlation.