Vol. 10, No. 4, 2021

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On a communication complexity problem in combinatorial number theory

Bence Bakos, Norbert Hegyvári and Máté Pálfy

Vol. 10 (2021), No. 4, 297–302
DOI: 10.2140/moscow.2021.10.297
Abstract

The original knapsack problem is well known to be NP-complete. In a multidimensional version, one have to decide whether a p k is in the sumset-sum of a set X k. In this paper, we are going to investigate a communication complexity problem related to this. We are also going to prove some results about the special case of the multidimensional knapsack problem, when the set X is in the form X = A1 × × Ak k, where Ai is a so-called regular set for every i = 1,2,,k.

Keywords
subset sums, communication complexity, matching in bipartite graph
Mathematical Subject Classification
Primary: 11B30, 11B39, 11B75
Milestones
Received: 27 July 2021
Revised: 21 October 2021
Accepted: 7 November 2021
Published: 17 January 2022
Authors
Bence Bakos
Institute of Mathematics
Eötvös University
Budapest
Hungary
Norbert Hegyvári
Institute of Mathematics
Eötvös University
Budapest
Hungary
Alfréd Rényi Institute of Mathematics
Budapest
Hungary
Máté Pálfy
Institute of Mathematics
Eötvös University
Budapest
Hungary