# hw5 - Computer Science 340 Reasoning about Computation...

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Computer Science 340 Reasoning about Computation Homework 5 Due at the beginning of class on Wednesday, October 24, 2007 This homework consists of 5 problems Problem 1 Consider the three-element list with the following initial configuration: ( x 1 , x 2 , x 3 ), (ie, x 1 is at the front). What is the cost of MTF for the access sequence: x 3 , x 2 , x 3 , x 2 . Prove that the optimal offline cost to serve the same access sequence is 8. Problem 2 Let MTF d be a variant of MTF that moves an accessed item at position i at least i/d - 1 positions closer to the front of the list. Show that for any static request sequence of size n , the cost is MTF d ( σ ) d (2 OPT C ( σ ) + OPT P ( σ ) - OPT F ( σ ) - n ) . (See handouts for meaning of notation.) Problem 3 Let ALG0 be any list accessing algorithm and let σ be any request sequence. Prove that there is an algorithm ALG1 that uses only paid transpositions (before the access) such that the cost of ALG0 and ALG1 are the same. (Don’t worry about how one would go implementing such an algorithm.) Consider a variant of the list accessing problem in which

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• Fall '07
• CharikarandChazelle
• Insertion Sort, Online algorithm, adversary, list accessing algorithm, better randomized algorithm

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