 
Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 5 Out: December 3, 2002
Due: December 10, 2002
1. Recall the BinPacking problem:
INPUT: A set of positive integers A = fa 1 : : : an g, a positive bin size B, and a positive integer k.
QUESTION: Can we partition A into k disjoint sets such that the sum of the integers in any set is at
most B.
(a) Use the SubsetSum problem to prove that BinPacking is NPComplete.
(b) Does your proof from part (a) show that BinPacking is strongly NPComplete? Explain why or
why not.
(c) Dene an appropriate optimization version of the BinPacking problem, and prove that if there is
a ( 3
2
)approximation to this problem, for any > 0, then P=NP.
2. [CLRS] 355: Parallel machine scheduling.
3. In class, we saw how to express the MaxFlow problem as a Linear Programming problem. In this
question, you are asked to extend this construction to a more general
ow problem, called the Multi
commodity Flow problem.
This is dened as follows. We are given a directed graph G with positive capacities C(e) on its edges,
