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CMPSCI 611: Advanced Algorithms Micah Adler

Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 5 Out: December 3, 2002
Due: December 10, 2002
1. Recall the Bin-Packing 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 Subset-Sum problem to prove that Bin-Packing is NP-Complete.
(b) Does your proof from part (a) show that Bin-Packing is strongly NP-Complete? Explain why or
why not.
(c) De ne an appropriate optimization version of the Bin-Packing problem, and prove that if there is
a ( 3
)-approximation to this problem, for any  > 0, then P=NP.
2. [CLRS] 35-5: Parallel machine scheduling.
3. In class, we saw how to express the Max-Flow 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 de ned as follows. We are given a directed graph G with positive capacities C(e) on its edges,


Source: Adler, Micah - Department of Computer Science, University of Massachusetts at Amherst


Collections: Computer Technologies and Information Sciences