CS648 Randomized Algorithms Semester II, 2007-08
Assignment 1
Due on : 30 January
Note : Give complete details of the analysis of your solution. Be very rigorous in providing any mathematical detail in support of your arguments. Also mention the Lemma/The
CS648 Randomized Algorithms Semester II, 2007-08.
Assignment 2
Due on : 3:00 PM, 19 February (before the lecture)
Note : Give complete details of the analysis of your solution. Be very rigorous in providing any mathematical detail in support of your argum
CS648 Randomized Algorithms Semester II, 2007-08.
Assignment 3
Due on : 7 March
Note : Give complete details of the analysis of your solution. Be very rigorous in providing any mathematical detail in support of your arguments. Also mention the Lemma/Theor
CS648 Randomized Algorithms Semester II, 2007-08.
Assignment 4
Due on : 1st April
Note : Give complete details of the analysis of your solution. Be very rigorous in providing any mathematical detail in support of your arguments. Also mention the Lemma/The
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CS648 Randomized Algorithms Lecture notes :Principle of deferred decision II Expected distance between two vertices in a complete graph with random edge weights
Principle of deferred decision : Let f be a function of n random variables and there is an und
CS648
Randomized Algorithms Lecture notes : 1
1
Elementary Probability Theory
Happening of unexpected events around us is not uncommon. It therefore makes sense to abandon the idea of a world with certainties and accept a world where we associate likeliho
CS648
Randomized Algorithms Lecture notes : 2
1
Some probability problems
Lemma 1.1 For a non-negative integer valued random variable X , E[X ] =
t=0
Pr[X > t]
Proof: Since X is a non-negative integer values random variable, the following equality holds.
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CS648 Randomized Algorithms Semester II, 2007-08
Practice problem sheet Note : More and more problems will be added to this sheet every week. Please attempt these problems on your own. This will help you internalise the techniques of this course. 1. Let X
CS648 Randomized Algorithms Semester II, 2007-08
Motivational problem sheet Note : These problems are for those students whose expectation from this course is at least little more than just getting a good grade. More and more problems will be added to thi
Solutions to Assignment 1
Anindya De Y4062 e-mail: cfw_anindya@cse.iitk.ac.in February 5, 2008
Randomized Select
Expected Number of Comparisons
Solution: Let X be a random variable which denotes the number of comparisons made during any random experiment.