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2015 | 29 | 1 | 93-117
Tytuł artykułu

Communication Complexity And Linearly Ordered Sets

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
29
Numer
1
Strony
93-117
Opis fizyczny
Daty
wydano
2015-09-01
otrzymano
2014-07-24
poprawiono
2015-03-21
online
2015-09-30
Twórcy
  • Institute of Mathematics, University of Silesia, Bankowa 14 40-007 Katowice, Poland, mkula@us.edu.pl
Bibliografia
  • [1] Ahlswede R., Cai N., Tamm U., Communication complexity in lattices, Appl. Math. Lett. 6 (1993), no. 6, 53–58.[Crossref]
  • [2] Babaioff M., Blumrosen L., Naor M., Schapira M., Informational overhead of incentive compatibility, in: Proc. 9th ACM Conference on Electronic Commerce, ACM, 2008, pp. 88–97.
  • [3] Björner A., Kalander J., Lindström B., Communication complexity of two decision problems, Discrete Appl. Math. 39 (1992), 161–163.
  • [4] Kushilevitz E., Nisan N., Communication complexity, Cambridge University Press, Cambridge, 1997.
  • [5] Lovasz L., Sachs M., Communication complexity and combinatorial lattice theory, J. Comput. System Sci. 47 (1993), 322–349.
  • [6] Mehlhorn K., Schmidt E., Las Vegas is better than determinism in VLSI and distributed computing, in: Proc. 14th Ann. ACM Symp. on Theory of Computing, ACM, 1982, pp. 330–337.
  • [7] Serwecińska M., Communication complexity in linear ordered sets, Bull. Sect. Logic 33 (2004), no. 4, 209–222.
  • [8] Yao A.C., Some complexity questions related to distributive computing, in: Proc. 11th Ann. ACM Symp. on Theory of Computing, ACM, 1979, pp. 209–213.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_amsil-2015-0008
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