Let f be a flow in a network, and let α be a real number. The scalar

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Let f be a flow in a network, and let Î± be a real number. The scalar flow product, denoted Î±f, is a function from V Ã— V to „ defined by

(af ) (u, ν) α.f(u, ν) Ξα

Prove that the flows in a network form a convex set. That is, show that if f1 and f2 are flows, then so is Î±f1 + (1 €“ Î±)f2 for all α in the range 0 ‰¤ α ‰¤ 1.

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Introduction to Algorithms

ISBN: 978-0262033848

3rd edition

Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest

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