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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2021.25

How to Send a Real Number Using a Single Bit (And Some Shared Randomness)

Authors: Ran Ben Basat, Michael Mitzenmacher, and Shay Vargaftik

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

We consider the fundamental problem of communicating an estimate of a real number x ∈ [0,1] using a single bit. A sender that knows x chooses a value X ∈ {0,1} to transmit. In turn, a receiver estimates x based on the value of X. The goal is to minimize the cost, defined as the worst-case (over the choice of x) expected squared error. We first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose optimal and near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions.

Cite as

Ran Ben Basat, Michael Mitzenmacher, and Shay Vargaftik. How to Send a Real Number Using a Single Bit (And Some Shared Randomness). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{benbasat_et_al:LIPIcs.ICALP.2021.25,
  author =	{Ben Basat, Ran and Mitzenmacher, Michael and Vargaftik, Shay},
  title =	{{How to Send a Real Number Using a Single Bit (And Some Shared Randomness)}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.25},
  URN =		{urn:nbn:de:0030-drops-140942},
  doi =		{10.4230/LIPIcs.ICALP.2021.25},
  annote =	{Keywords: Randomized Algorithms, Approximation Algorithms, Shared Randomness, Distributed Protocols, Estimation, Subtractive Dithering}
}

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DOI: 10.4230/LIPIcs.DISC.2020.14

Distributed Dispatching in the Parallel Server Model

Authors: Guy Goren, Shay Vargaftik, and Yoram Moses

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract

With the rapid increase in the size and volume of cloud services and data centers, architectures with multiple job dispatchers are quickly becoming the norm. Load balancing is a key element of such systems. Nevertheless, current solutions to load balancing in such systems admit a paradoxical behavior in which more accurate information regarding server queue lengths degrades performance due to herding and detrimental incast effects. Indeed, both in theory and in practice, there is a common doubt regarding the value of information in the context of multi-dispatcher load balancing. As a result, both researchers and system designers resort to more straightforward solutions, such as the power-of-two-choices to avoid worst-case scenarios, potentially sacrificing overall resource utilization and system performance. A principal focus of our investigation concerns the value of information about queue lengths in the multi-dispatcher setting. We argue that, at its core, load balancing with multiple dispatchers is a distributed computing task. In that light, we propose a new job dispatching approach, called Tidal Water Filling, which addresses the distributed nature of the system. Specifically, by incorporating the existence of other dispatchers into the decision-making process, our protocols outperform previous solutions in many scenarios. In particular, when the dispatchers have complete and accurate information regarding the server queue lengths, our policies significantly outperform all existing solutions.

Cite as

Guy Goren, Shay Vargaftik, and Yoram Moses. Distributed Dispatching in the Parallel Server Model. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{goren_et_al:LIPIcs.DISC.2020.14,
  author =	{Goren, Guy and Vargaftik, Shay and Moses, Yoram},
  title =	{{Distributed Dispatching in the Parallel Server Model}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.14},
  URN =		{urn:nbn:de:0030-drops-130929},
  doi =		{10.4230/LIPIcs.DISC.2020.14},
  annote =	{Keywords: Distributed load balancing, Join the Shortest Queue, Tidal Water Filling,  Parallel Server Model}
}

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How to Send a Real Number Using a Single Bit (And Some Shared Randomness)

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Distributed Dispatching in the Parallel Server Model

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