Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems
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. Somewhat surprisingly, we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.
Cite
@article{arxiv.2409.15970,
title = {Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems},
author = {Bingbing Hu and Adam Polak},
journal= {arXiv preprint arXiv:2409.15970},
year = {2025}
}