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Optimal Speedup on a Low-Degree Multi-Core Parallel Architecture (LoPRAM)

Authors: Alejandro Lopez-Ortiz, Reza Dorrigiv, and Alejandro Salinger

Published in: Dagstuhl Seminar Proceedings, Volume 8081, Data Structures (2008)

Abstract

We propose a new model with small degreee of parallelism that reflects current and future multicore architectures in practice. The model is based on the PRAM architecture and hence it inherits many of its interesting theoretical properties. The key observations and differences are that the degree of parallelism (i.e. number of processors or cores) is bounded by O(log n), the synchronization model is looser and the use of parallelism is at a higher level unless explicitly specified otherwise. Surprisingly, these three rather minor variants result in a model in which obtaining work optimal algorithms is significantly easier than for the PRAM. The new model is called Low-degree PRAM or LoPRAM for short. Lastly we observe that there are thresholds in complexity of programming at p=O(log n) and p=O(sqrt(n)) and provide references for specific problems for which this threshold has been formally proven.

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Alejandro Lopez-Ortiz, Reza Dorrigiv, and Alejandro Salinger. Optimal Speedup on a Low-Degree Multi-Core Parallel Architecture (LoPRAM). In Data Structures. Dagstuhl Seminar Proceedings, Volume 8081, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{lopezortiz_et_al:DagSemProc.08081.3,
  author =	{Lopez-Ortiz, Alejandro and Dorrigiv, Reza and Salinger, Alejandro},
  title =	{{Optimal Speedup on a Low-Degree Multi-Core Parallel Architecture (LoPRAM)}},
  booktitle =	{Data Structures},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8081},
  editor =	{Lars Arge and Robert Sedgewick and Raimund Seidel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08081.3},
  URN =		{urn:nbn:de:0030-drops-15315},
  doi =		{10.4230/DagSemProc.08081.3},
  annote =	{Keywords: PRAM, multicore architectures, parallelism, algorithms, dynamic programming, divide and conquer}
}

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DOI: 10.4230/DagSemProc.06421.4

Adaptive Analysis of On-line Algorithms

Authors: Reza Dorrigiv and Alejandro Lopez-Ortiz

Published in: Dagstuhl Seminar Proceedings, Volume 6421, Robot Navigation (2007)

Abstract

On-line algorithms are usually analyzed using competitive analysis, in which the performance of on-line algorithm on a sequence is normalized by the performance of the optimal on-line algorithm on that sequence. In this paper we introduce adaptive/cooperative analysis as an alternative general framework for the analysis of on-line algorithms. This model gives promising results when applied to two well known on-line problems, paging and list update. The idea is to normalize the performance of an on-line algorithm by a measure other than the performance of the on-line optimal algorithm OPT. We show that in many instances the perform of OPT on a sequence is a coarse approximation of the difficulty or complexity of a given input. Using a finer, more natural measure we can separate paging and list update algorithms which were otherwise undistinguishable under the classical model. This createas a performance hierarchy of algorithms which better reflects the intuitive relative strengths between them. Lastly, we show that, surprisingly, certain randomized algorithms which are superior to MTF in the classical model are not so in the adaptive case. This confirms that the ability of the on-line adaptive algorithm to ignore pathological worst cases can lead to algorithms that are more efficient in practice.

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Reza Dorrigiv and Alejandro Lopez-Ortiz. Adaptive Analysis of On-line Algorithms. In Robot Navigation. Dagstuhl Seminar Proceedings, Volume 6421, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{dorrigiv_et_al:DagSemProc.06421.4,
  author =	{Dorrigiv, Reza and Lopez-Ortiz, Alejandro},
  title =	{{Adaptive Analysis of On-line Algorithms}},
  booktitle =	{Robot Navigation},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6421},
  editor =	{S\'{a}ndor Fekete and Rudolf Fleischer and Rolf Klein and Alejandro Lopez-Ortiz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06421.4},
  URN =		{urn:nbn:de:0030-drops-8696},
  doi =		{10.4230/DagSemProc.06421.4},
  annote =	{Keywords: On-line algorithms, paging, adaptive/cooperative analysis}
}

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Documents authored by Dorrigiv, Reza

Optimal Speedup on a Low-Degree Multi-Core Parallel Architecture (LoPRAM)

Abstract

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Adaptive Analysis of On-line Algorithms

Abstract

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