Recent progress on combinatorics and algorithms for low discrepancy roundings

Takeshi Tokuyama

doi:10.1007/s00373-007-0700-9

Recent progress on combinatorics and algorithms for low discrepancy roundings

Takeshi Tokuyama

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Given a [0,1]-valued n-dimensional vector a = (a ₁, a ₂, . . . , a _n )∈ [0,1] ^V indexed by a set V = {v ₁, v ₂, . . . , v _n }, we consider the problem of approximating a by a binary (i.e., {0,1}-valued) vector α = (α ₁, α ₂, . . . , α _n ) {0,1} ^V under the discrepancy measure with respect to a hypergraph H = (V, F). We are interested in the properties of low-discrepancy roundings. Especially, we survey recent works on the combinatorial properties of a global rounding; that is, rounding whose discrepancy is less than 1.

Original language	English
Pages (from-to)	359-378
Number of pages	20
Journal	Graphs and Combinatorics
Volume	23
Issue number	SUPPL. 1
DOIs	https://doi.org/10.1007/s00373-007-0700-9
Publication status	Published - 2007 Jun 1

Keywords

Algorithm
Discrepancy
Graph
Hypergraph
Matrix
Rounding

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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KW - Matrix

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Recent progress on combinatorics and algorithms for low discrepancy roundings

Abstract

Keywords

ASJC Scopus subject areas

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