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Communication Complexity Theory: Thirty-Five Years of Set Disjointness

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

The set disjointness problem features k communicating parties and k subsets S 1,S 2,…,S k  ⊆ {1,2,…,n}. No single party knows all k subsets, and the objective is to determine with minimal communication whether the k subsets have nonempty intersection. The important special case k = 2 corresponds to two parties trying to determine whether their respective sets intersect. The study of the set disjointness problem spans almost four decades and offers a unique perspective on the remarkable evolution of communication complexity theory. We discuss known results on the communication complexity of set disjointness in the deterministic, nondeterministic, randomized, unbounded-error, and multiparty models, emphasizing the variety of mathematical techniques involved.

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Authors and Affiliations

  1. University of California, Los Angeles, USA

    Alexander A. Sherstov

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  1. Alexander A. Sherstov
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Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Sherstov, A.A. (2014). Communication Complexity Theory: Thirty-Five Years of Set Disjointness. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_3

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  • DOI: https://doi.org/10.1007/978-3-662-44522-8_3

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