Individual Communication Complexity
Harry Buhrman (CWI, University of Amsterdam), Hartmut Klauck (IAS,, Princeton), Nikolai Vereshchagin (Moscow University), Paul Vitanyi (CWI and, University of Amsterdam)
TL;DR
This paper develops a new theoretical framework for analyzing the communication complexity of individual inputs using Kolmogorov complexity, moving beyond traditional worst-case and average-case analyses.
Contribution
It introduces the theory of individual communication complexity, considering various protocol types and expressing results through Kolmogorov complexity, a novel approach in the field.
Findings
Established foundational results for individual communication complexity
Connected Kolmogorov complexity with communication protocols
Analyzed different protocol models and help bits
Abstract
We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with and without help bits. The results are expressed in trems of Kolmogorov complexity.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Complexity and Algorithms in Graphs · Machine Learning and Algorithms