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I/O complexity: The red-blue pebble game

Authors:

Hong Jia-Wei,

H. T. KungAuthors Info & Claims

STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

Pages 326 - 333

https://doi.org/10.1145/800076.802486

Published: 11 May 1981 Publication History

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Abstract

In this paper, the red-blue pebble game is proposed to model the input-output complexity of algorithms. Using the pebble game formulation, a number of lower bound results for the I/O requirement are proven. For example, it is shown that to perform the n-point FFT or the ordinary n×n matrix multiplication algorithm with O(S) memory, at least Ω(n log n/log S) or Ω(n³/@@@@S), respectively, time is needed for the I/O. Similar results are obtained for algorithms for several other problems. All of the lower bounds presented are the best possible in the sense that they are achievable by certain decomposition schemes.

Results of this paper may provide insight into the difficult task of balancing I/O and computation in special-purpose system designs. For example, for the n-point FFT, the lower bound on I/O time implies that an S-point device achieving a speed-up ratio of order log S over the conventional O(n log n) time implementation is all one can hope for.

References

[1]

Cook, S.A. and Sethi, R. Storage Requirements for Deterministic Polynomial Time Recognizable Languages. J. Comp. and Sys. Sci. 13:25-37, 1976.

Google Scholar

[2]

Floyd, R.W. Permuting Information in Idealized Two-Level Storage. In Miller, R.E. and Thatcher, J.W. (editor), Complexity of Computer Computations, pages 105-109. Plenum Press, New York, 1972.

Crossref

Google Scholar

[3]

Harary, F. Graph Theory. Addison-Wesley, Reading, Massachusetts, 1969.

Google Scholar

[4]

Hopcroft, J.E., Paul, W. and Valiant, L.G. On Time Versus Space. Journal of the ACM 24:332-337, 1977.

Digital Library

Google Scholar

[5]

Kernighan, B.W. and Lin, S. An Effective Heuristic Procedure for Partitioning Graphs. Bell Systems Technical Journal 49:291-308, February, 1970.

Crossref

Google Scholar

[6]

Knuth, D. E. The Art of Computer Programming. Volume 3: Sorting and Searching. Addison-Wesley, Reading, Massachusetts, 1973.

Digital Library

Google Scholar

[7]

Kung, H.T. Special-Purpose Devices for Signal and Image Processing: An Opportunity in VLSI. Technical Report, Carnegie-Mellon University, Department of Computer Science, July, 1980. Presented at SPIE's 24th Annual Technical Symposium, San Diego, California, July 1980. The final version of the paper is to be published in the Symposium Proceedings.

Google Scholar

[8]

Pippenger, N. Pebbling. In Proc. the Fifth IBM Symposium on Mathematical Foundations of Computer Science. Academic & Scientific Programs, IBM Japan, May, 1980.

Google Scholar

[9]

Rosenberg, A. L. Private communication.

Google Scholar

[10]

Song, S.W. I/O Complexity, and Design of Special-Purpose Hardware for Sorting. VLSI Document V075, Carnegie-Mellon University, Department of Computer Science, February, 1981.

Google Scholar

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Eyraud-Dubois LIooss GLangou JRastello FAgrawal KPetrank E(2024)Tightening I/O Lower Bounds through the Hourglass Dependency PatternProceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3626183.3659986(183-193)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3626183.3659986
Huang QTsai PEmer JParashar A(2024)Mind the Gap: Attainable Data Movement and Operational Intensity Bounds for Tensor Algorithms2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA)10.1109/ISCA59077.2024.00021(150-166)Online publication date: 29-Jun-2024
https://doi.org/10.1109/ISCA59077.2024.00021
Nissim RSchwartz OShabo R(2024)Challenges in Parallel Matrix Chain MultiplicationJob Scheduling Strategies for Parallel Processing10.1007/978-3-031-74430-3_7(120-140)Online publication date: 21-Dec-2024
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Index Terms

I/O complexity: The red-blue pebble game
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
  2. Mathematical analysis
    1. Numerical analysis
      1. Computation of transforms
2. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Sorting and searching

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STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

May 1981

390 pages

ISBN:9781450373920

DOI:10.1145/800076

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 11 May 1981

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On dynamic bit-probe complexity

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