LecX4 - 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 Birthday Paradox 2/11/10 COT 6936 2 Birthday Paradox • To achieve probability ± ² , we need: ± m 2 /2n ± ln 2 ± m ± sqrt{2n ln 2} • In a room with at least 23 people, the probability that at least two people have the same birthday is more than ² . 2/11/10 COT 6936 3
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2 Balls and Bins Model • Throw m balls into n bins • Location of each ball chosen independently and uniformly at random • Interesting questions to ask ± How many balls in a bin on the average? ± How many bins are empty? ± How many balls in the fullest bin? ± How many bins are expected to have > 1 ball in it? • Applications: Hashing with Chaining 1/12/10 COT 6936 4 Birthday Paradox Average Size of a Chain in Hash Table • Let N = # of possible hash values • Let k = # items stored in the hash table
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LecX4 - COT 6936: Topics in Algorithms Giri Narasimhan ECS...

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