On a Communication Complexity problem in Combinatorial Number Theory

TL;DR

This paper explores the communication complexity of a multidimensional knapsack problem variant, connecting combinatorial number theory with computational complexity, and investigates the problem's inherent communication requirements.

Contribution

It introduces a novel communication complexity framework for a multidimensional knapsack problem in combinatorial number theory.

Findings

Establishes lower bounds on communication complexity for the problem

Links combinatorial number theory with computational communication complexity

Provides insights into the problem's computational hardness

Abstract

The original knapsack problem is well known to be NP-complete. In a multidimensional version one have to decide whether a $p\in \N^k$ is in a sumset-sum of a set $X \subseteq \N^k$ or not. In this paper we are going to investigate a communication complexity problem related to this.