2 Search Results for "Berger, Alon"

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.104

Optimal Non-Adaptive Cell Probe Dictionaries and Hashing

Authors: Kasper Green Larsen, Rasmus Pagh, Giuseppe Persiano, Toniann Pitassi, Kevin Yeo, and Or Zamir

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We present a simple and provably optimal non-adaptive cell probe data structure for the static dictionary problem. Our data structure supports storing a set of n key-value pairs from [u]× [u] using s words of space and answering key lookup queries in t = O(lg(u/n)/lg(s/n)) non-adaptive probes. This generalizes a solution to the membership problem (i.e., where no values are associated with keys) due to Buhrman et al. We also present matching lower bounds for the non-adaptive static membership problem in the deterministic setting. Our lower bound implies that both our dictionary algorithm and the preceding membership algorithm are optimal, and in particular that there is an inherent complexity gap in these problems between no adaptivity and one round of adaptivity (with which hashing-based algorithms solve these problems in constant time). Using the ideas underlying our data structure, we also obtain the first implementation of a n-wise independent family of hash functions with optimal evaluation time in the cell probe model.

Cite as

Kasper Green Larsen, Rasmus Pagh, Giuseppe Persiano, Toniann Pitassi, Kevin Yeo, and Or Zamir. Optimal Non-Adaptive Cell Probe Dictionaries and Hashing. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 104:1-104:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{larsen_et_al:LIPIcs.ICALP.2024.104,
  author =	{Larsen, Kasper Green and Pagh, Rasmus and Persiano, Giuseppe and Pitassi, Toniann and Yeo, Kevin and Zamir, Or},
  title =	{{Optimal Non-Adaptive Cell Probe Dictionaries and Hashing}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{104:1--104:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.104},
  URN =		{urn:nbn:de:0030-drops-202471},
  doi =		{10.4230/LIPIcs.ICALP.2024.104},
  annote =	{Keywords: non-adaptive, cell probe, dictionary, hashing}
}

Document

DOI: 10.4230/LIPIcs.DISC.2018.11

Integrated Bounds for Disintegrated Storage

Authors: Alon Berger, Idit Keidar, and Alexander Spiegelman

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract

We point out a somewhat surprising similarity between non-authenticated Byzantine storage, coded storage, and certain emulations of shared registers from smaller ones. A common characteristic in all of these is the inability of reads to safely return a value obtained in a single atomic access to shared storage. We collectively refer to such systems as disintegrated storage, and show integrated space lower bounds for asynchronous regular wait-free emulations in all of them. In a nutshell, if readers are invisible, then the storage cost of such systems is inherently exponential in the size of written values; otherwise, it is at least linear in the number of readers. Our bounds are asymptotically tight to known algorithms, and thus justify their high costs.

Cite as

Alon Berger, Idit Keidar, and Alexander Spiegelman. Integrated Bounds for Disintegrated Storage. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{berger_et_al:LIPIcs.DISC.2018.11,
  author =	{Berger, Alon and Keidar, Idit and Spiegelman, Alexander},
  title =	{{Integrated Bounds for Disintegrated Storage}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.11},
  URN =		{urn:nbn:de:0030-drops-98009},
  doi =		{10.4230/LIPIcs.DISC.2018.11},
  annote =	{Keywords: storage, coding, lower bounds, space complexity, register emulations}
}

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