Efficient construction of a small hitting set for combinatorial rectangles in high dimension

Nati Linial; Michael Luby; Michael Saks; David Zuckerman

doi:10.1145/167088.167166

Efficient construction of a small hitting set for combinatorial rectangles in high dimension

Nati Linial, Michael Luby, Michael Saks, David Zuckerman

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

Given d, m and €, we deterministically produce a sequence of points S that hits every combinatorial rectangle in [m]d of volume at least 6. Both the running time of the algorithm and ISI are polynomial in m log(d) /€. This algorithm has applications to deterministic constructions of small sample spaces for general multivalued random variables.

Original language	American English
Title of host publication	Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993
Publisher	Association for Computing Machinery
Pages	258-267
Number of pages	10
ISBN (Electronic)	0897915917
DOIs	https://doi.org/10.1145/167088.167166
State	Published - 1 Jun 1993
Event	25th Annual ACM Symposium on Theory of Computing, STOC 1993 - San Diego, United States Duration: 16 May 1993 → 18 May 1993

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	Part F129585
ISSN (Print)	0737-8017

Conference

Conference	25th Annual ACM Symposium on Theory of Computing, STOC 1993
Country/Territory	United States
City	San Diego
Period	16/05/93 → 18/05/93

Bibliographical note

Funding Information:
*Hebrew University, Computer Science Department, Jerusalem Israel. Research partially done while visiting the International Computer Science Institute. tInternational Computer Science Institute and UC Berkeley. Research partially supported by NSF Grant CCR-9016468 and grant No. 89-00312 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. tDepartment of Mathematics, Rutgers University and Department of CSE, UCSD. Supported in part by NSF under grant CCR-8911388 and by AFOSR grants AFOSR-89-0512 AFOSR-90-OO08. Research partially done while visiting the International Computer Science Institute. ~Laboratory for Computer Science, MIT, Cambridge, Massachusetts. Research partially supported by an NSF Postdoctoral Fellowship. Research partially done while visiting the International Computer Science Institute.

Publisher Copyright:
© 1993 ACM.

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10.1145/167088.167166

Cite this

Linial, N., Luby, M., Saks, M., & Zuckerman, D. (1993). Efficient construction of a small hitting set for combinatorial rectangles in high dimension. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993 (pp. 258-267). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129585). Association for Computing Machinery. https://doi.org/10.1145/167088.167166

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abstract = "Given d, m and €, we deterministically produce a sequence of points S that hits every combinatorial rectangle in [m]d of volume at least 6. Both the running time of the algorithm and ISI are polynomial in m log(d) /€. This algorithm has applications to deterministic constructions of small sample spaces for general multivalued random variables.",

author = "Nati Linial and Michael Luby and Michael Saks and David Zuckerman",

note = "Funding Information: *Hebrew University, Computer Science Department, Jerusalem Israel. Research partially done while visiting the International Computer Science Institute. tInternational Computer Science Institute and UC Berkeley. Research partially supported by NSF Grant CCR-9016468 and grant No. 89-00312 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. tDepartment of Mathematics, Rutgers University and Department of CSE, UCSD. Supported in part by NSF under grant CCR-8911388 and by AFOSR grants AFOSR-89-0512 AFOSR-90-OO08. Research partially done while visiting the International Computer Science Institute. ~Laboratory for Computer Science, MIT, Cambridge, Massachusetts. Research partially supported by an NSF Postdoctoral Fellowship. Research partially done while visiting the International Computer Science Institute. Publisher Copyright: {\textcopyright} 1993 ACM.; 25th Annual ACM Symposium on Theory of Computing, STOC 1993 ; Conference date: 16-05-1993 Through 18-05-1993",

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Linial, N, Luby, M, Saks, M & Zuckerman, D 1993, Efficient construction of a small hitting set for combinatorial rectangles in high dimension. in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. Part F129585, Association for Computing Machinery, pp. 258-267, 25th Annual ACM Symposium on Theory of Computing, STOC 1993, San Diego, United States, 16/05/93. https://doi.org/10.1145/167088.167166

Efficient construction of a small hitting set for combinatorial rectangles in high dimension. / Linial, Nati; Luby, Michael; Saks, Michael et al.
Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993. Association for Computing Machinery, 1993. p. 258-267 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129585).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Efficient construction of a small hitting set for combinatorial rectangles in high dimension

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