9 Search Results for "Ben-Basat, Ran"

Document
DOI: 10.4230/LIPIcs.DISC.2025.40
On the Randomized Locality of Matching Problems in Regular Graphs

Authors: Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
The main goal in distributed symmetry-breaking is to understand the locality of problems: the radius of the neighborhood that a node must explore to determine its part of a global solution. In this work, we study the locality of matching problems in the family of regular graphs, which is one of the main benchmarks for establishing lower bounds on the locality of symmetry-breaking problems, as well as for obtaining classification results. Our main results are summarized as follows: 1) Approximate matching: We develop randomized algorithms to show that (1 + ε)-approximate matching in regular graphs is truly local, i.e., the locality depends only on ε and is independent of all other graph parameters. Furthermore, as long as the degree Δ is not very small (namely, as long as Δ ≥ poly(1/ε)), this dependence is only logarithmic in 1/ε. This stands in sharp contrast to maximal matching in regular graphs which requires some dependence on the number of nodes n or the degree Δ. 2) Maximal matching: Our techniques further allow us to establish a strong separation between the node-averaged complexity and worst-case complexity of maximal matching in regular graphs, by showing that the former is only O(1). Central to our main technical contribution is a novel martingale-based analysis for the ≈ 40-year-old algorithm by Luby. In particular, our analysis shows that applying one round of Luby’s algorithm on the line graph of a Δ-regular graph results in an almost Δ/2-regular graph.
Cite as

Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang. On the Randomized Locality of Matching Problems in Regular Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoury_et_al:LIPIcs.DISC.2025.40,
  author =	{Khoury, Seri and Purohit, Manish and Schild, Aaron and Wang, Joshua R.},
  title =	{{On the Randomized Locality of Matching Problems in Regular Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{40:1--40:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.40},
  URN =		{urn:nbn:de:0030-drops-248570},
  doi =		{10.4230/LIPIcs.DISC.2025.40},
  annote =	{Keywords: regular graphs, maximum matching, augmenting paths, distributed algorithms, Luby’s algorithm, martingales}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.23
Distributed Recoverable Sketches

Authors: Diana Cohen, Roy Friedman, and Rana Shahout

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
Sketches are commonly used in computer systems and network monitoring tools to provide efficient query executions while maintaining a compact data representation. Switches and routers maintain sketches to track statistical characteristics of the network traffic. The availability of such data is essential for the network analysis as a whole. Consequently, being able to recover sketches is critical following a switch crash. In this paper, we explore how nodes in a network environment can cooperate to recover sketch data whenever any of them crashes. In particular, we focus on frequency estimation linear sketches, such as the Count-Min Sketch. We consider various approaches to ensure data reliability and explore the trade-offs between space consumption, runtime overheads, and traffic during recovery, which we point out as design guidelines. Besides different aspects of efficacy, we design a modular system for ease of maintenance and further scaling. A key aspect we examine is how nodes update each other about their sketch content as it evolves over time. In particular, we compare between periodic full updates vs. incremental updates. We also examine several data structures to economically represent and encode a batch of latest changes. Our framework is generic, and other data structures can be plugged-in via an abstract API as long as they implement the corresponding API methods.
Cite as

Diana Cohen, Roy Friedman, and Rana Shahout. Distributed Recoverable Sketches. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cohen_et_al:LIPIcs.OPODIS.2024.23,
  author =	{Cohen, Diana and Friedman, Roy and Shahout, Rana},
  title =	{{Distributed Recoverable Sketches}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.23},
  URN =		{urn:nbn:de:0030-drops-225594},
  doi =		{10.4230/LIPIcs.OPODIS.2024.23},
  annote =	{Keywords: Sketches, Stream Processing, Distributed Recovery, Incremental Updates, Sketch Partitioning}
}
Document
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}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.5
Optimal Distributed Covering Algorithms

Authors: Ran Ben-Basat, Guy Even, Ken-ichi Kawarabayashi, and Gregory Schwartzman

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f+epsilon). Let Delta denote the maximum degree in the hypergraph. Our algorithm runs in the congest model and requires O(log{Delta} / log log Delta) rounds, for constants epsilon in (0,1] and f in N^+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. Thus adding another member to the exclusive family of provably optimal distributed algorithms. For constant values of f and epsilon, our algorithm improves over the (f+epsilon)-approximation algorithm of [Fabian Kuhn et al., 2006] whose running time is O(log Delta + log W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an f-approximation for the problem in O(f log n) rounds, improving over the classical result of [Samir Khuller et al., 1994] that achieves a running time of O(f log^2 n). Finally, for weighted vertex cover (f=2) our algorithm achieves a deterministic running time of O(log n), matching the randomized previously best result of [Koufogiannakis and Young, 2011]. We also show that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (f+epsilon)-approximate integral solution in O((1+f/log n)* ((log Delta)/(log log Delta) + (f * log M)^{1.01}* log epsilon^{-1}* (log Delta)^{0.01})) rounds, where f bounds the number of variables in a constraint, Delta bounds the number of constraints a variable appears in, and M=max {1, ceil[1/a_{min}]}, where a_{min} is the smallest normalized constraint coefficient. This improves over the results of [Fabian Kuhn et al., 2006] for the integral case, which combined with rounding achieves the same guarantees in O(epsilon^{-4}* f^4 * log f * log(M * Delta)) rounds.
Cite as

Ran Ben-Basat, Guy Even, Ken-ichi Kawarabayashi, and Gregory Schwartzman. Optimal Distributed Covering Algorithms. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{benbasat_et_al:LIPIcs.DISC.2019.5,
  author =	{Ben-Basat, Ran and Even, Guy and Kawarabayashi, Ken-ichi and Schwartzman, Gregory},
  title =	{{Optimal Distributed Covering Algorithms}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.5},
  URN =		{urn:nbn:de:0030-drops-113129},
  doi =		{10.4230/LIPIcs.DISC.2019.5},
  annote =	{Keywords: Distributed Algorithms, Approximation Algorithms, Vertex Cover, Set Cover}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.6
Parameterized Distributed Algorithms

Authors: Ran Ben-Basat, Ken-ichi Kawarabayashi, and Gregory Schwartzman

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
In this work, we initiate a thorough study of graph optimization problems parameterized by the output size in the distributed setting. In such a problem, an algorithm decides whether a solution of size bounded by k exists and if so, it finds one. We study fundamental problems, including Minimum Vertex Cover (MVC), Maximum Independent Set (MaxIS), Maximum Matching (MaxM), and many others, in both the LOCAL and CONGEST distributed computation models. We present lower bounds for the round complexity of solving parameterized problems in both models, together with optimal and near-optimal upper bounds. Our results extend beyond the scope of parameterized problems. We show that any LOCAL (1+epsilon)-approximation algorithm for the above problems must take Omega(epsilon^{-1}) rounds. Joined with the (epsilon^{-1}log n)^{O(1)} rounds algorithm of [Ghaffari et al., 2017] and the Omega (sqrt{(log n)/(log log n)}) lower bound of [Fabian Kuhn et al., 2016], the lower bounds match the upper bound up to polynomial factors in both parameters. We also show that our parameterized approach reduces the runtime of exact and approximate CONGEST algorithms for MVC and MaxM if the optimal solution is small, without knowing its size beforehand. Finally, we propose the first o(n^2) rounds CONGEST algorithms that approximate MVC within a factor strictly smaller than 2.
Cite as

Ran Ben-Basat, Ken-ichi Kawarabayashi, and Gregory Schwartzman. Parameterized Distributed Algorithms. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{benbasat_et_al:LIPIcs.DISC.2019.6,
  author =	{Ben-Basat, Ran and Kawarabayashi, Ken-ichi and Schwartzman, Gregory},
  title =	{{Parameterized Distributed Algorithms}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.6},
  URN =		{urn:nbn:de:0030-drops-113135},
  doi =		{10.4230/LIPIcs.DISC.2019.6},
  annote =	{Keywords: Distributed Algorithms, Approximation Algorithms, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.54
Approximate Query Processing over Static Sets and Sliding Windows

Authors: Ran Ben Basat, Seungbum Jo, Srinivasa Rao Satti, and Shubham Ugare

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to support approximate versions of the operations rank(i) (i.e., computing sum_{j <= i} B[j]) and select(i) (i.e., finding min{p|rank(p) >= i}) queries. We study multiple types of approximations (allowing an error in the query or the result) and present lower bounds and succinct data structures for several variants of the problem. We also extend our model to sliding windows, in which we process a stream of elements and compute suffix sums. This is a generalization of the window summation problem that allows the user to specify the window size at query time. Here, we provide an algorithm that supports updates and queries in constant time while requiring just (1+o(1)) factor more space than the fixed-window summation algorithms.
Cite as

Ran Ben Basat, Seungbum Jo, Srinivasa Rao Satti, and Shubham Ugare. Approximate Query Processing over Static Sets and Sliding Windows. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 54:1-54:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{benbasat_et_al:LIPIcs.ISAAC.2018.54,
  author =	{Ben Basat, Ran and Jo, Seungbum and Satti, Srinivasa Rao and Ugare, Shubham},
  title =	{{Approximate Query Processing over Static Sets and Sliding Windows}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{54:1--54:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.54},
  URN =		{urn:nbn:de:0030-drops-100027},
  doi =		{10.4230/LIPIcs.ISAAC.2018.54},
  annote =	{Keywords: Streaming, Algorithms, Sliding window, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.34
Give Me Some Slack: Efficient Network Measurements

Authors: Ran Ben Basat, Gil Einziger, and Roy Friedman

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W(1+tau) where tau is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Omega(W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct, the slack model enables a further asymptotic improvement. The main focus of the paper is on the widely studied Basic-Summing problem of computing the sum of the last W integers from {0,1 ...,R} in a stream. While it is known that Omega(W log R) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant tau. Specifically, for tau=Theta(1), we present a space lower bound of Omega(log(RW)) bits. Additionally, we show an Omega(log (W/epsilon)) lower bound for RW epsilon additive approximations and a Omega(log (W/epsilon)+log log R) bits lower bound for (1+epsilon) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [Mayur Datar et al., 2002] for (1+epsilon)-multiplicative approximation that requires O(epsilon^(-1) log(RW)log log (RW)) space and performs updates in O(log (RW)) worst case time. Finally, we show asymptotic improvements for the Count-Distinct, General-Summing and Maximum problems.
Cite as

Ran Ben Basat, Gil Einziger, and Roy Friedman. Give Me Some Slack: Efficient Network Measurements. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{benbasat_et_al:LIPIcs.MFCS.2018.34,
  author =	{Ben Basat, Ran and Einziger, Gil and Friedman, Roy},
  title =	{{Give Me Some Slack: Efficient Network Measurements}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul 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.MFCS.2018.34},
  URN =		{urn:nbn:de:0030-drops-96165},
  doi =		{10.4230/LIPIcs.MFCS.2018.34},
  annote =	{Keywords: Streaming, Network Measurements, Statistics, Lower Bounds}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.163
Brief Announcement: Give Me Some Slack: Efficient Network Measurements

Authors: Ran Ben Basat, Gil Einziger, and Roy Friedman

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W(1+tau) where tau is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Omega(W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct, the slack model enables a further asymptotic improvement. The main focus of our paper [{Ben Basat} et al., 2017] is on the widely studied Basic-Summing problem of computing the sum of the last W integers from {0,1 ...,R} in a stream. While it is known that Omega(W log{R}) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant tau. Specifically, for tau=Theta(1), we present a space lower bound of Omega(log(RW)) bits. Additionally, we show an Omega(log ({W/epsilon})) lower bound for RW epsilon additive approximations and a Omega(log ({W/epsilon})+log log{R}) bits lower bound for (1+epsilon) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [Mayur Datar et al., 2002] for (1+epsilon)-multiplicative approximation that requires O(epsilon^{-1} log ({RW})log log ({RW})) space and performs updates in O(log ({RW})) worst case time. Finally, we show asymptotic improvements for the Count-Distinct, General-Summing and Maximum problems.
Cite as

Ran Ben Basat, Gil Einziger, and Roy Friedman. Brief Announcement: Give Me Some Slack: Efficient Network Measurements. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 163:1-163:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{benbasat_et_al:LIPIcs.ICALP.2018.163,
  author =	{Ben Basat, Ran and Einziger, Gil and Friedman, Roy},
  title =	{{Brief Announcement: Give Me Some Slack: Efficient Network Measurements}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{163:1--163:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.163},
  URN =		{urn:nbn:de:0030-drops-91672},
  doi =		{10.4230/LIPIcs.ICALP.2018.163},
  annote =	{Keywords: Streaming, Algorithms, Sliding window, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.11
Efficient Summing over Sliding Windows

Authors: Ran Ben Basat, Gil Einziger, Roy Friedman, and Yaron Kassner

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of Omega(1/epsilon + log(W)) memory bits for Wepsilon-additive approximations is derived. This is followed by an algorithm whose memory consumption is O(1/epsilon + log(W)) bits, indicating that the algorithm is optimal and that the bound is tight. Next, the more general problem of maintaining a sum of the last W integers, each in the range of {0, 1, ..., R}, is addressed. The paper shows that approximating the sum within an additive error of RW epsilon can also be done using Theta(1/epsilon + log(W)) bits for epsilon = Omega(1/W). For epsilon = o(1/W), we present a succinct algorithm which uses B(1 + o(1)) bits, where B = Theta(W*log(1/(W*epsilon))) is the derived lower bound. We show that all lower bounds generalize to randomized algorithms as well. All algorithms process new elements and answer queries in O(1) worst-case time.
Cite as

Ran Ben Basat, Gil Einziger, Roy Friedman, and Yaron Kassner. Efficient Summing over Sliding Windows. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{benbasat_et_al:LIPIcs.SWAT.2016.11,
  author =	{Ben Basat, Ran and Einziger, Gil and Friedman, Roy and Kassner, Yaron},
  title =	{{Efficient Summing over Sliding Windows}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.11},
  URN =		{urn:nbn:de:0030-drops-60241},
  doi =		{10.4230/LIPIcs.SWAT.2016.11},
  annote =	{Keywords: Streaming, Statistics, Lower Bounds}
}
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