Aug 20, 2017

The first-fit decreasing (FFD) approximation algorithm for the bin-packing problem starts by sorting the items in nonincreasing order of their sizes and then acts as the first-fit algorithm.

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The first-fit decreasing (FFD) approximation algorithm for the bin-packing problem starts by sorting the items in nonincreasing order of their sizes and then acts as the first-fit algorithm.

a. Apply FFD to the instance

and determine whether the solution obtained is optimal.

b. Does FFD always yield an optimal solution? Justify your answer.

c. Prove that FFD is a 1.5-approximation algorithm.

d. Run an experiment to determine which of the two algorithms—FF or FFD—yields more accurate approximations on a random sample of the problem’s instances.


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