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

Amihood Amir; Emanuel Dar

doi:10.1016/s0020-0190(97)00047-1

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

Amihood Amir
, Emanuel Dar

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	95-101
Number of pages	7
Journal	Information Processing Letters
Volume	62
Issue number	2
DOIs	https://doi.org/10.1016/s0020-0190(97)00047-1
State	Published - 28 Apr 1997

Bibliographical note

Funding Information:
* Corresponding author. Email: [email protected]. Partially sup-port by NSF grant CCR-92-23699 and Israel Ministry of Science and Arts grant 6297. ’ Email: [email protected].

Funding

* Corresponding author. Email: [email protected]. Partially sup-port by NSF grant CCR-92-23699 and Israel Ministry of Science and Arts grant 6297. ’ Email: [email protected].

Funders	Funder number
Israel Ministry of Science and Arts	6297
National Science Foundation	CCR-92-23699

Keywords

Algorithms
Biased number generation
Random sampling
Random set generation

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10.1016/s0020-0190(97)00047-1

Cite this

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title = "An improved deterministic algorithm for generating different many-element random samples",

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.",

keywords = "Algorithms, Biased number generation, Random sampling, Random set generation",

author = "Amihood Amir and Emanuel Dar",

note = "Funding Information: * Corresponding author. Email: [email protected]. Partially sup-port by NSF grant CCR-92-23699 and Israel Ministry of Science and Arts grant 6297. {\textquoteright} Email: [email protected].",

year = "1997",

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doi = "10.1016/s0020-0190(97)00047-1",

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AU - Dar, Emanuel

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N2 - 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.

AB - 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.

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KW - Biased number generation

KW - Random sampling

KW - Random set generation

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

Abstract

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Keywords

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