AMS/MBA 546 (Fall, 2010)
Estie Arkin
Network Flows
Homework Set # 8
Due 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 solution
x
∗
of a minimum cost flow problem, suppose that we redefine
arc capacities
u
′
as follows:
u
′
ij
=
braceleftbigg
u
ij
if
x
∗
ij
=
u
ij
∞
otherwise
Show that
x
∗
is also an optimal solution of the minimum cost flow problem with the arc capacities as
u
′
.
2). [12.4] The Bin Packing paroblem is as follows: There are
n
items of weight
a
1
,a
2
,...,a
n
(assume that
0
≤
a
i
≤
1). What is the minimum number of Bins each of total weight at most 1, are needed to pack all
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 Fall '08
 Arkin,E
 Bipartite graph, Bin packing problem, Packing problem, Estie Arkin, Bin Packing

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