Discrepancy sets and pseudorandom generators for combinatorial rectangles

Roy Armoni; Michael Saks; Avi Wigderson; Shiyu Zhou

Discrepancy sets and pseudorandom generators for combinatorial rectangles

Roy Armoni^*
, Michael Saks
, Avi Wigderson
, Shiyu Zhou

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Conference article › peer-review

38 Scopus citations

Abstract

A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)-size sample space that approximates the volume of any combinatorial rectangle in [n]ⁿ to within o(1) error (improving on the constructions of [EGLNV92]). The construction extends the techniques of [LLSZ95] for the analogous hitting set problem, most notably via discrepancy preserving reductions.

Original language	English
Pages (from-to)	412-421
Number of pages	10
Journal	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
State	Published - 1996
Event	Proceedings of the 1996 37th Annual Symposium on Foundations of Computer Science - Burlington, VT, USA Duration: 14 Oct 1996 → 16 Oct 1996

Cite this

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title = "Discrepancy sets and pseudorandom generators for combinatorial rectangles",

abstract = "A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)-size sample space that approximates the volume of any combinatorial rectangle in [n]n to within o(1) error (improving on the constructions of [EGLNV92]). The construction extends the techniques of [LLSZ95] for the analogous hitting set problem, most notably via discrepancy preserving reductions.",

author = "Roy Armoni and Michael Saks and Avi Wigderson and Shiyu Zhou",

year = "1996",

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pages = "412--421",

journal = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

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note = "Proceedings of the 1996 37th Annual Symposium on Foundations of Computer Science ; Conference date: 14-10-1996 Through 16-10-1996",

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AU - Armoni, Roy

AU - Saks, Michael

AU - Wigderson, Avi

AU - Zhou, Shiyu

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N2 - A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)-size sample space that approximates the volume of any combinatorial rectangle in [n]n to within o(1) error (improving on the constructions of [EGLNV92]). The construction extends the techniques of [LLSZ95] for the analogous hitting set problem, most notably via discrepancy preserving reductions.

AB - A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)-size sample space that approximates the volume of any combinatorial rectangle in [n]n to within o(1) error (improving on the constructions of [EGLNV92]). The construction extends the techniques of [LLSZ95] for the analogous hitting set problem, most notably via discrepancy preserving reductions.

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SN - 0272-5428

SP - 412

EP - 421

JO - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

JF - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

T2 - Proceedings of the 1996 37th Annual Symposium on Foundations of Computer Science

Y2 - 14 October 1996 through 16 October 1996

ER -

Discrepancy sets and pseudorandom generators for combinatorial rectangles

Abstract

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