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# LecXX - COT 6936: Topics in Algorithms Giri Narasimhan ECS...

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1 2/11/10 COT 6936 1 COT 6936: Topics in Algorithms Giri Narasimhan ECS 254A / EC 2443; Phone: x3748 giri@cs.fiu.edu http://www.cs.fiu.edu/~giri/teach/COT6936_S10.html https://online.cis.fiu.edu/portal/course/view.php?id=427 How to Analyze Online Algorithms? • Competitive analysis ± Compare with optimal offline algorithm (OPT) • Algorithm A is ± -competitive if there exists constants b such that for every sequence of inputs ² : ± cost A ( ² ) ± ± cost OPT ( ² ) + b 2/11/10 COT 6936 2 Ski Rental Problem • Should Dr. Raju buy skis or rent them? ± Rental is \$A per trip ± Purchase costs \$B • Idea: ± Rent for m trips, where • m = B/A ± Then purchase skis • Analysis: ± Competitiveness ratio = 2. Why ? 2/11/10 COT 6936 3

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2 How to Analyze Rand Online Algorithms? • Algorithm A is ± -competitive if there exists constants b such that for every sequence of inputs ² : ± cost A ( ² ) ± ± cost OPT ( ² ) + b • Randomized Algorithm R is ± -competitive if there exists constants b such that for every sequence of inputs ² : ± E[cost R ( ² )] ± ± cost OPT ( ² ) + b 2/11/10 COT 6936 4 Adversary provides request sequence at start Randomized Online algorithms • Lower bound does not apply to randomized algorithms ± Lower bound on randomized algorithms = H k • Proof uses 2 main principles ± Cover time of a random walk on K k+1 is kH k ± Lower bound on competitiveness of randomized
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## This note was uploaded on 02/18/2012 for the course CIS 6936 taught by Professor Giri during the Spring '12 term at FIU.

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LecXX - COT 6936: Topics in Algorithms Giri Narasimhan ECS...

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