research-article

An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound

Authors:

Shashwat GargAuthors Info & Claims

SIAM Journal on Computing, Volume 48, Issue 2

Pages 534 - 553

https://doi.org/10.1137/17M1126795

Published: 01 January 2019 Publication History

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 $O((t \log n)^{1/2})$, 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.

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Cited By

Bansal NRohwedder LSvensson OLeonardi SGupta A(2022)Flow time scheduling and prefix Beck-FialaProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520077(331-342)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520077
Hopkins SRaghavendra PShetty ALeonardi SGupta A(2022)Matrix discrepancy from Quantum communicationProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519954(637-648)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519954

Index Terms

An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
  2. Mathematical analysis
    1. Numerical analysis
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Computing

SIAM Journal on Computing Volume 48, Issue 2

DOI:10.1137/smjcat.48.2

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© 2019, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2019

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Cited By

Bansal NRohwedder LSvensson OLeonardi SGupta A(2022)Flow time scheduling and prefix Beck-FialaProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520077(331-342)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520077
Hopkins SRaghavendra PShetty ALeonardi SGupta A(2022)Matrix discrepancy from Quantum communicationProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519954(637-648)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519954

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