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

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.

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