An improved deterministic algorithm for generating different many-element random samples

Amihood Amir, Emanuel Dar

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of deterministically selecting s uniformly random different m-element subsets of {1 , . . . , k}. The only known lower bound for the time to solve this problem is the trivial Ω(sm). The best two previously known solutions are of time O(sm3 log m log log m) and O(s(k + m)), respectively. In this paper we present an algorithm whose time complexity is O(s2m2 + sm2 log m log log m + sm log sm). Thus, for s < m log m log log m this algorithm is the fastest known deterministic algorithm. The main idea of the algorithm is using a uniform random number generator to efficiently construct biased random numbers.

Original languageEnglish
Pages (from-to)95-101
Number of pages7
JournalInformation Processing Letters
Volume62
Issue number2
DOIs
StatePublished - 28 Apr 1997

Bibliographical note

Funding Information:
* Corresponding author. Email: amir@cs.biu.ac.il. Partially sup-port by NSF grant CCR-92-23699 and Israel Ministry of Science and Arts grant 6297. ’ Email: dar@macs.biu.ac.il.

Keywords

  • Algorithms
  • Biased number generation
  • Random sampling
  • Random set generation

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