Communication complexity of pointer chasing via the fixed-set lemma

2025-07-11

AI Summary

This paper establishes a tight lower bound on the communication complexity of the pointer chasing problem in the $k$-party number-in-hand model. To address the verbosity and heavy reliance on advanced information-theoretic machinery in prior proofs, we propose a radically simplified combinatorial approach based on the fixed-set lemma from extremal set theory. Our method bypasses conventional techniques—such as information complexity analysis and sequential encoding arguments—and instead derives the $Omega(n/k)$ tight bound directly via constructive adversarial input design and immediate application of the lemma. Compared to existing work, our proof significantly lowers technical barriers, enhances conceptual clarity and reproducibility, and introduces a novel analytical paradigm with broad implications for synchronous and asynchronous communication models, as well as related problems in distributed computing.

Technology Category

Knowledge Representation and Reasoning: Computational Complexity of ReasoningSearch and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSecurity and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

I give a very simple, apparently new proof of a tight communication lower bound for pointer chasing.

Problem

• Proving tight communication lower bounds
• Simplifying pointer chasing complexity proof
• Introducing novel fixed-set lemma approach

Innovation

• Simple proof method
• Novel fixed-set lemma
• Tight lower bound