Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

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)

Succinct Sampling from Discrete Distributions

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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