AMS/MBA 546 (Fall, 2010)Estie ArkinNetwork FlowsHomework Set # 8Due Thursday, November 18, 2010.Suggested reading Chapters 9, 12 and Section 11.12 (Unimodularity Property) of [AMO].1). [9.30] With respect to an optimal solutionx∗of a minimum cost flow problem, suppose that we redefinearc capacitiesu′as follows:u′ij=braceleftbigguijifx∗ij=uij∞otherwiseShow thatx∗is also an optimal solution of the minimum cost flow problem with the arc capacities asu′.2). [12.4] The Bin Packing paroblem is as follows: There arenitems of weighta1,a2,...,an(assume that0≤ai≤1). What is the minimum number of Bins each of total weight at most 1, are needed to pack all
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Bipartite graph, Bin packing problem, Packing problem, Estie Arkin, Bin Packing