On the Local Communication Complexity of Counting and Modular Arithmetic
Bala Kalyanasundaram, Calvin Newport

TL;DR
This paper explores the local communication complexity in multi-party computation, showing that small local communication suffices for counting, sorting, searching, and modular arithmetic, while establishing some lower bounds.
Contribution
It introduces new lower bounds for local complexity and demonstrates that constant local communication can compute various functions including symmetric, sorting, and modular operations.
Findings
Counting the number of 1's among first 17 bits requires more than 1 bit per player.
Constant local complexity suffices for counting, sorting, and searching.
Modular arithmetic operations and GCD can be computed with constant local communication.
Abstract
In standard number-in-hand multi-party communication complexity, performance is measured as the total number of bits transmitted globally in the network. In this paper, we study a variation called local communication complexity in which performance instead measures the maximum number of bits sent or received at any one player. We focus on a simple model where players, each with one input bit, execute a protocol by exchanging messages to compute a function on the input bits. We ask what can and cannot be solved with a small local communication complexity in this setting. We begin by establishing a non-trivial lower bound on the local complexity for a specific function by proving that counting the number of 's among the first input bits distributed among the participants requires a local complexity strictly greater than . We further investigate whether harder counting…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Distributed systems and fault tolerance · Cryptography and Data Security
