Noisy Boolean Hidden Matching with Applications
Michael Kapralov, Amulya Musipatla, Jakab Tardos, David P. Woodruff,, Samson Zhou

TL;DR
This paper introduces a noisy variant of the Boolean Hidden Matching problem to establish stronger streaming lower bounds for graph problems, especially for graphs with bounded component diameters, advancing understanding of streaming complexity.
Contribution
It proposes the noisy BHM and BHH problems, providing new techniques to prove higher lower bounds in streaming models for specific graph classes.
Findings
Higher lower bounds for graph approximation problems in streaming models.
Proves that classifying certain graphs requires linear space in insertion-only streams.
Demonstrates the effectiveness of noisy BHM in complexity lower bounds.
Abstract
The Boolean Hidden Matching (BHM) problem, introduced in a seminal paper of Gavinsky et. al. [STOC'07], has played an important role in the streaming lower bounds for graph problems such as triangle and subgraph counting, maximum matching, MAX-CUT, Schatten -norm approximation, maximum acyclic subgraph, testing bipartiteness, -connectivity, and cycle-freeness. The one-way communication complexity of the Boolean Hidden Matching problem on a universe of size is , resulting in lower bounds for constant factor approximations to several of the aforementioned graph problems. The related (and, in fact, more general) Boolean Hidden Hypermatching (BHH) problem introduced by Verbin and Yu [SODA'11] provides an approach to proving higher lower bounds of for integer . Reductions based on Boolean Hidden Hypermatching…
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Videos
Noisy Boolean Hidden Matching with Applications· youtube
Taxonomy
TopicsComplexity and Algorithms in Graphs · Distributed systems and fault tolerance · Optimization and Search Problems
