## Abstract

Graph coloring is a fundamental problem with wide reaching applications in various areas including ata mining and databases, e.g., in parallel query optimization. In recent years, there has been a growing interest in solving various graph coloring problems in the streaming model. The initial algorithms in this line of work are all crucially randomized, raising natural questions about how important a role randomization plays in streaming graph coloring. A couple of very recent works prove that deterministic or even adversarially robust coloring algorithms (that work on streams whose updates may depend on the algorithm's past outputs) are considerably weaker than standard randomized ones. However, there is still a significant gap between the upper and lower bounds for the number of colors needed (as a function of the maximum degree ") for robust coloring and multipass deterministic coloring. We contribute to this line of work by proving the following results. In the deterministic semi-streaming (i.e., O(n · polylog n) space) regime, we present an algorithm that achieves a combinatorially optimal ("+1)-coloring using O(logΔlog log") passes. This improves upon the prior O(")-coloring algorithm of Assadi, Chen, and Sun (STOC 2022) at the cost of only an O(log log") factor in the number of passes. In the adversarially robust semi-streaming regime, we design an O("5/2)-coloring algorithm that improves upon the previously best O("3)-coloring algorithm of Chakrabarti, Ghosh, and Stoeckl (ITCS 2022). Further, we obtain a smooth colors/space tradeoff that improves upon another algorithm of the said work: whereas their algorithm uses O("2) colors and O(n"1/2) space, ours, in particular, achieves (i)∼O("2) colors in O(n"1/3) space, and (ii)∼O("7/4) colors in O(n"1/2) space.

Original language | English (US) |
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Title of host publication | PODS 2023 - Proceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems |

Publisher | Association for Computing Machinery |

Pages | 141-153 |

Number of pages | 13 |

ISBN (Electronic) | 9798400701276 |

DOIs | |

State | Published - Jun 18 2023 |

Event | 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2023 - Seattle, United States Duration: Jun 18 2023 → Jun 23 2023 |

### Publication series

Name | Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems |
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### Conference

Conference | 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2023 |
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Country/Territory | United States |

City | Seattle |

Period | 6/18/23 → 6/23/23 |

## All Science Journal Classification (ASJC) codes

- Software
- Information Systems
- Hardware and Architecture

## Keywords

- adversarial robustness
- data streams
- graph coloring