An algorithm for komlós conjecture matching Banaszczyk's bound

Nikhil Bansal, Daniel Dadush, Shashwat Garg

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
34 Downloads (Pure)

Abstract

We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((tlog n) 1 / 2 ), matching the best known nonconstructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t 1 / 2 log n) bound. The result also extends to the more general Komlós setting and gives an algorithmic O(log 1 / 2 n) bound.

Original languageEnglish
Pages (from-to)534-553
Number of pages20
JournalSIAM Journal on Computing
Volume48
Issue number2
DOIs
Publication statusPublished - 30 Apr 2019

Keywords

  • Discrepancy
  • Random walk
  • Semidefinite programming
  • semidefinite programming
  • random walk
  • discrepancy

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