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Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems

Authors Bingbing Hu , Adam Polak

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Complexity classes
Keywords
  • Fine-grained complexity
  • OMv hypothesis
  • reductions
  • equivalence class

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Abstract

Most of the known tight lower bounds for dynamic problems are based on the Online Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and understood as some more popular hypotheses in fine-grained complexity. It would be desirable to base hardness of dynamic problems on a more believable hypothesis. We propose analogues of the OMv Hypothesis for variants of matrix multiplication that are known to be harder than Boolean product in the offline setting, namely: equality, dominance, min-witness, min-max, and bounded monotone min-plus products. These hypotheses are a priori weaker assumptions than the standard (Boolean) OMv Hypothesis and yet we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.

Cite As Get BibTex

Bingbing Hu and Adam Polak. Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.54

Author Details

Bingbing Hu
  • University of California San Diego, La Jolla, CA, USA
Adam Polak
  • Bocconi University, Milan, Italy

Funding

Part of this work was done when both authors were at Max Planck Institute for Informatics.

Acknowledgements

We thank anonymous reviewers for pointing us to the literature on the cell-probe model and for many useful hints on improving the manuscript.

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