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Annales Mathematicae Silesianae

Editor-in-Chief: Sablik, Maciej

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Communication Complexity And Linearly Ordered Sets

Mieczysław Kula / Małgorzata Serwecińska
Published Online: 2015-09-30 | DOI: https://doi.org/10.1515/amsil-2015-0008


The paper is devoted to the communication complexity of lattice operations in linearly ordered finite sets. All well known techniques ([4, Chapter 1]) to determine the communication complexity of the infimum function in linear lattices disappoint, because a gap between the lower and upper bound is equal to O(log2 n), where n is the cardinality of the lattice. Therefore our aim will be to investigate the communication complexity of the function more carefully. We consider a family of so called interval protocols and we construct the interval protocols for the infimum. We prove that the constructed protocols are optimal in the family of interval protocols. It is still open problem to compute the communication complexity of constructed protocols but the numerical experiments show that their complexity is less than the complexity of known protocols for the infimum function.

(2010) Mathematics Subject Classification:: 68Q17; 68Q25

Key words and phrases:: communication complexity; linear lattice; communication protocol; interval protocol


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About the article

Received: 2014-07-24

Revised: 2015-03-21

Published Online: 2015-09-30

Published in Print: 2015-09-01

Citation Information: Annales Mathematicae Silesianae, Volume 29, Issue 1, Pages 93–117, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2015-0008.

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© Mieczysław Kula et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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