assign2 - CS648 Randomized Algorithms Semester II 2007-08...

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Unformatted text preview: 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 arguments. Also mention the Lemma/Theorem you use. Only a printed version of the softcopy of this assignment will be accepted, and no submissions will be accepted after the deadline. 1. (7) Set Balancing Given an n × n matrix A all of whose entries are 0 or 1, our aim is to compute a column vector b ∈ {- 1 , +1 } n minimizing || Ab || ∞ . Here is a surprisingly simple algorithm A: Construct the vector b as follows : each entry of b is independently and equiprobably chosen from {- 1 , +1 } . Show that with very high probability, || Ab || ∞ is going to be O ( √ n ln n ) . 2. (8) Analysing a randomized process by partitioning it into stages Consider the following randomized process. There are n bins and n players, and each player has an...
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