Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Tuesday, January 28, 2014, 12:15 pm
Duration: 30 minutes
Location: OAT S15/S16/S17
Speaker: Karl Bringmann (MPI Saarbrücken)
We revisit the classic problem of sampling from a discrete distribution: Given n positive numbers p1,...,pn, the task is to build a data structure that allows sampling i with probability proportional to pi. The classic solution to this problem is Walker's alias method that takes O(n) preprocessing time and O(1) query time for one sample, which is optimal.
We study the space requirements of this problem, effectively considering it in the world of succinct data structures. For two standard models of succinct data structures, we improve upon the space requirements of Walker's alias method (while keeping the preprocessing and query time asymptotically). Moreover, we complement our data structures with matching lower bounds. On the one hand, our results improve upon the space requirement of the classic solution for a fundamental sampling problem, on the other hand, they provide the strongest known separation between two standard models of succinct data structures for any data structure problem.
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