4 Search Results for "Johnson, Rob"

Document
DOI: 10.4230/LIPIcs.ESA.2022.16
When Are Cache-Oblivious Algorithms Cache Adaptive? A Case Study of Matrix Multiplication and Sorting

Authors: Arghya Bhattacharya, Abiyaz Chowdhury, Helen Xu, Rathish Das, Rezaul A. Chowdhury, Rob Johnson, Rishab Nithyanand, and Michael A. Bender

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Cache-adaptive algorithms are a class of algorithms that achieve optimal utilization of dynamically changing memory. These memory fluctuations are the norm in today’s multi-threaded shared-memory machines and time-sharing caches. Bender et al. [Bender et al., 2014] proved that many cache-oblivious algorithms are optimally cache-adaptive, but that some cache-oblivious algorithms can be relatively far from optimally cache-adaptive on worst-case memory fluctuations. This worst-case gap between cache obliviousness and cache adaptivity depends on a highly-structured, adversarial memory profile. Existing cache-adaptive analysis does not predict the relative performance of cache-oblivious and cache-adaptive algorithms on non-adversarial profiles. Does the worst-case gap appear in practice, or is it an artifact of an unrealistically powerful adversary? This paper sheds light on the question of whether cache-oblivious algorithms can effectively adapt to realistically fluctuating memory sizes; the paper focuses on matrix multiplication and sorting. The two matrix-multiplication algorithms in this paper are canonical examples of "(a, b, c)-regular" cache-oblivious algorithms, which underlie much of the existing theory on cache-adaptivity. Both algorithms have the same asymptotic I/O performance when the memory size remains fixed, but one is optimally cache-adaptive, and the other is not. In our experiments, we generate both adversarial and non-adversarial memory workloads. The performance gap between the algorithms for matrix multiplication grows with problem size (up to 3.8×) on the adversarial profiles, but the gap does not grow with problem size (stays at 2×) on non-adversarial profiles. The sorting algorithms in this paper are not "(a, b, c)-regular," but they have been well-studied in the classical external-memory model when the memory size does not fluctuate. The relative performance of a non-oblivious (cache-aware) sorting algorithm degrades with the problem size: it incurs up to 6 × the number of disk I/Os compared to an oblivious adaptive algorithm on both adversarial and non-adversarial profiles. To summarize, in all our experiments, the cache-oblivious matrix-multiplication and sorting algorithms that we tested empirically adapt well to memory fluctuations. We conjecture that cache-obliviousness will empirically help achieve adaptivity for other problems with similar structures.
Cite as

Arghya Bhattacharya, Abiyaz Chowdhury, Helen Xu, Rathish Das, Rezaul A. Chowdhury, Rob Johnson, Rishab Nithyanand, and Michael A. Bender. When Are Cache-Oblivious Algorithms Cache Adaptive? A Case Study of Matrix Multiplication and Sorting. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 16:1-16:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhattacharya_et_al:LIPIcs.ESA.2022.16,
  author =	{Bhattacharya, Arghya and Chowdhury, Abiyaz and Xu, Helen and Das, Rathish and Chowdhury, Rezaul A. and Johnson, Rob and Nithyanand, Rishab and Bender, Michael A.},
  title =	{{When Are Cache-Oblivious Algorithms Cache Adaptive? A Case Study of Matrix Multiplication and Sorting}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.16},
  URN =		{urn:nbn:de:0030-drops-169543},
  doi =		{10.4230/LIPIcs.ESA.2022.16},
  annote =	{Keywords: Cache-adaptive algorithms, cache-oblivious algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.11
A Dynamic Space-Efficient Filter with Constant Time Operations

Authors: Ioana O. Bercea and Guy Even

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
A dynamic dictionary is a data structure that maintains sets of cardinality at most n from a given universe and supports insertions, deletions, and membership queries. A filter approximates membership queries with a one-sided error that occurs with probability at most ε. The goal is to obtain dynamic filters that are space-efficient (the space is 1+o(1) times the information-theoretic lower bound) and support all operations in constant time with high probability. One approach to designing filters is to reduce to the retrieval problem. When the size of the universe is polynomial in n, this approach yields a space-efficient dynamic filter as long as the error parameter ε satisfies log(1/ε) = ω(log log n). For the case that log(1/ε) = O(log log n), we present the first space-efficient dynamic filter with constant time operations in the worst case (whp). In contrast, the space-efficient dynamic filter of Pagh et al. [Anna Pagh et al., 2005] supports insertions and deletions in amortized expected constant time. Our approach employs the classic reduction of Carter et al. [Carter et al., 1978] on a new type of dictionary construction that supports random multisets.
Cite as

Ioana O. Bercea and Guy Even. A Dynamic Space-Efficient Filter with Constant Time Operations. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 11:1-11:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bercea_et_al:LIPIcs.SWAT.2020.11,
  author =	{Bercea, Ioana O. and Even, Guy},
  title =	{{A Dynamic Space-Efficient Filter with Constant Time Operations}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.11},
  URN =		{urn:nbn:de:0030-drops-122582},
  doi =		{10.4230/LIPIcs.SWAT.2020.11},
  annote =	{Keywords: Data Structures}
}
Document
DOI: 10.4230/DagRep.9.3.39
Theoretical Foundations of Storage Systems (Dagstuhl Seminar 19111)

Authors: Martin Farach-Colton, Inge Li Gørtz, Rob Johnson, and Donald E. Porter

Published in: Dagstuhl Reports, Volume 9, Issue 3 (2019)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 19111 "Theoretical Foundations of Storage Systems." This seminar brought together researchers from two distinct communities - algorithms researchers with an interest in external memory and systems researchers with an interest in storage - with the objective of improving the design of future storage systems.
Cite as

Martin Farach-Colton, Inge Li Gørtz, Rob Johnson, and Donald E. Porter. Theoretical Foundations of Storage Systems (Dagstuhl Seminar 19111). In Dagstuhl Reports, Volume 9, Issue 3, pp. 39-51, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@Article{farachcolton_et_al:DagRep.9.3.39,
  author =	{Farach-Colton, Martin and G{\o}rtz, Inge Li and Johnson, Rob and Porter, Donald E.},
  title =	{{Theoretical Foundations of Storage Systems (Dagstuhl Seminar 19111)}},
  pages =	{39--51},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{9},
  number =	{3},
  editor =	{Farach-Colton, Martin and G{\o}rtz, Inge Li and Johnson, Rob and Porter, Donald E.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.3.39},
  URN =		{urn:nbn:de:0030-drops-112909},
  doi =		{10.4230/DagRep.9.3.39},
  annote =	{Keywords: Storage Systems, External Memory Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.2
Fragile Complexity of Comparison-Based Algorithms

Authors: Peyman Afshani, Rolf Fagerberg, David Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, and Nodari Sitchinava

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes part in. We give a number of upper and lower bounds on the fragile complexity for fundamental problems, including Minimum, Selection, Sorting and Heap Construction. The results include both deterministic and randomized upper and lower bounds, and demonstrate a separation between the two settings for a number of problems. The depth of a comparator network is a straight-forward upper bound on the worst case fragile complexity of the corresponding fragile algorithm. We prove that fragile complexity is a different and strictly easier property than the depth of comparator networks, in the sense that for some problems a fragile complexity equal to the best network depth can be achieved with less total work and that with randomization, even a lower fragile complexity is possible.
Cite as

Peyman Afshani, Rolf Fagerberg, David Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, and Nodari Sitchinava. Fragile Complexity of Comparison-Based Algorithms. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 2:1-2:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2019.2,
  author =	{Afshani, Peyman and Fagerberg, Rolf and Hammer, David and Jacob, Riko and Kostitsyna, Irina and Meyer, Ulrich and Penschuck, Manuel and Sitchinava, Nodari},
  title =	{{Fragile Complexity of Comparison-Based Algorithms}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.2},
  URN =		{urn:nbn:de:0030-drops-111235},
  doi =		{10.4230/LIPIcs.ESA.2019.2},
  annote =	{Keywords: Algorithms, comparison based algorithms, lower bounds}
}
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