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Unformatted text preview: 15-750HW 0115-750 — Graduate Algorithms — Spring 2009Miller and Dinitz and TangwongsanAssignment 0 Due date: January 23Some Reminders:•Read the Policies section on the course web site before you start working on this assignment.Collaboration isnotpermitted for this assignment.•You should refrain from using outside sources when solving these problems. For each problem,state whether you have seen it before. If you have questions, contact the course staff.•We prefer that you type up your solutions (preferably using LaTeX). You may neatly hand-write your solutions, but if we have trouble reading them you will be required to type upfuture solutions.1Asymptotic Notation[10 points] For each list of functions, order them according to increasing asymptotic growth. Pro-vide a brief argument justifying each successive step in the ordering. Your answers should looksomething like:n1/2< n= 5n < n2. Don’t forget to mention iff(n) = Θ(g(n)).Disclaimer:itisnotstandard notation to writen1/2< n= 5n < n2under big-O notation. Nor is it standardto write Θ(n1/2) =o(n) = Θ(5n) =o(n2). When writing a paper, it would be better to say“n1/2=o(n) andn= Θ(5n) and 5n=o(n2),” but this would be longer for you to write and for usto grade.List 1, fast growing functions: 23n,32n,n!,nlog*n,nn√logn.List 2, slow growing functions: 2log*n,log*(22n),2√logn,log log√n,log(n5)Recall that log*(n) (the “log star” function) calculates how many times you would need to take the...
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This document was uploaded on 11/03/2009.
- Spring '09