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DOI: 10.4230/LIPIcs.ITCS.2019.64

A New Approach to Multi-Party Peer-to-Peer Communication Complexity

Authors: Adi Rosén and Florent Urrutia

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract

We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and then, in order to exemplify their effectiveness, we use them to prove two lower bounds. The more elaborate one is a tight lower bound of Omega(kn) on the multi-party peer-to-peer randomized communication complexity of the k-player, n-bit function Disjointness, Disj_k^n. The other one is a tight lower bound of Omega(kn) on the multi-party peer-to-peer randomized communication complexity of the k-player, n-bit bitwise parity function, Par_k^n. Both lower bounds hold when n=Omega(k). The lower bound for Disj_k^n improves over the lower bound that can be inferred from the result of Braverman et al. (FOCS 2013), which was proved in the coordinator model and can yield a lower bound of Omega(kn/log k) in the peer-to-peer model. To the best of our knowledge, our lower bounds are the first tight (non-trivial) lower bounds on communication complexity in the natural peer-to-peer multi-party setting. In addition to the above results for communication complexity, we also prove, using the same tools, an Omega(n) lower bound on the number of random bits necessary for the (information theoretic) private computation of the function Disj_k^n.

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Adi Rosén and Florent Urrutia. A New Approach to Multi-Party Peer-to-Peer Communication Complexity. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rosen_et_al:LIPIcs.ITCS.2019.64,
  author =	{Ros\'{e}n, Adi and Urrutia, Florent},
  title =	{{A New Approach to Multi-Party Peer-to-Peer Communication Complexity}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{64:1--64:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.64},
  URN =		{urn:nbn:de:0030-drops-101576},
  doi =		{10.4230/LIPIcs.ITCS.2019.64},
  annote =	{Keywords: communication complexity, multi-party communication complexity, peer-to-peer communication complexity, information complexity, private computation}
}

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DOI: 10.4230/LIPIcs.MFCS.2016.57

Multi-Party Protocols, Information Complexity and Privacy

Authors: Iordanis Kerenidis, Adi Rosén, and Florent Urrutia

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

We introduce the new measure of Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of randomness they require in the context of information-theoretic private computations. We are able to use this measure directly in the natural asynchronous message-passing peer-to-peer model and show a number of interesting properties and applications of our new notion: the Public Information Complexity is a lower bound on the Communication Complexity and an upper bound on the Information Complexity; the difference between the Public Information Complexity and the Information Complexity provides a lower bound on the amount of randomness used in a protocol; any communication protocol can be compressed to its Public Information Cost; an explicit calculation of the zero-error Public Information Complexity of the k-party, n-bit Parity function, where a player outputs the bit-wise parity of the inputs. The latter result establishes that the amount of randomness needed for a private protocol that computes this function is Omega(n).

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Iordanis Kerenidis, Adi Rosén, and Florent Urrutia. Multi-Party Protocols, Information Complexity and Privacy. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{kerenidis_et_al:LIPIcs.MFCS.2016.57,
  author =	{Kerenidis, Iordanis and Ros\'{e}n, Adi and Urrutia, Florent},
  title =	{{Multi-Party Protocols, Information Complexity and Privacy}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.57},
  URN =		{urn:nbn:de:0030-drops-64696},
  doi =		{10.4230/LIPIcs.MFCS.2016.57},
  annote =	{Keywords: multi-party protocols, information theory, communication complexity, multi-party private computation (MPC), randomness}
}

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A New Approach to Multi-Party Peer-to-Peer Communication Complexity

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Multi-Party Protocols, Information Complexity and Privacy

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