Towards Multi-Pass Streaming Lower Bounds for Optimal Approximation of Max-Cut

Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, Zhao Song, Huacheng Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We consider the Max-Cut problem, asking how much space is needed by a streaming algorithm in order to estimate the value of the maximum cut in a graph. This problem has been extensively studied over the last decade, and we now have a near-optimal lower bound for one-pass streaming algorithms, showing that they require linear space to guarantee a better-than-2 approximation [50, 52]. This result relies on a lower bound for the cycle-finding problem, showing that it is hard for a one-pass streaming algorithm to find a cycle in a union of matchings. The end-goal of our research is to prove a similar lower bound for multi-pass streaming algorithms that guarantee a better-than-2 approximation for Max-Cut, a highly challenging open problem. In this paper, we take a significant step in this direction, showing that even o(log n)-pass streaming algorithms need nΩ(1) space to solve the cycle-finding problem. Our proof is quite involved, dividing the cycles in the graph into “short” and “long” cycles, and using tailor-made lower bound techniques to handle each case.

Original languageEnglish (US)
Title of host publication34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023
PublisherAssociation for Computing Machinery
Pages878-924
Number of pages47
ISBN (Electronic)9781611977554
StatePublished - 2023
Event34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 - Florence, Italy
Duration: Jan 22 2023Jan 25 2023

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2023-January

Conference

Conference34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023
Country/TerritoryItaly
CityFlorence
Period1/22/231/25/23

All Science Journal Classification (ASJC) codes

  • Software
  • General Mathematics

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