Structure in Communication Complexity and Constant-Cost Complexity Classes

Hamed Hatami; Pooya Hatami

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arXiv · 2401.14623

Structure in Communication Complexity and Constant-Cost Complexity Classes

Hamed Hatami·Pooya Hatami

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Abstract

Several theorems and conjectures in communication complexity state or speculate that the complexity of a matrix in a given communication model is controlled by a related analytic or algebraic matrix parameter, e.g., rank, sign-rank, discrepancy, etc. The forward direction is typically easy as the structural implications of small complexity often imply a bound on some matrix parameter. The challenge lies in establishing the reverse direction, which requires understanding the structure of Boolean matrices for which a given matrix parameter is small or large. We will discuss several research directions that align with this overarching theme.

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Hamed Hatami, Pooya Hatami. 2024-01-26. Structure in Communication Complexity and Constant-Cost Complexity Classes. https://arxiv.org/abs/2401.14623

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