Recent progress on combinatorics and algorithms for low discrepancy roundings

Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)359-378
Number of pages20
JournalGraphs and Combinatorics
Volume23
Issue numberSUPPL. 1
DOIs
Publication statusPublished - 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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