Square meshes are not always optimal

Amotz Bar-Noy; David Peleg

doi:10.1145/72935.72951

Square meshes are not always optimal

Amotz Bar-Noy, David Peleg

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

In this paper we consider mesh connected computers with multiple buses, providing broadcast facilities along rows and columns. A tight bound of 0(n?) is established for the number of rounds required for semigroup computations on n values distributed on a 2-dimensional rectangular mesh of size n with a bus on every row and column. The upper bound is obtained for a skewed rectangular mesh of dimensions n3/8 × n5/8 This result is to be contrasted with the tight bound of θ(n1/6) for the same problem on the square (n1/2 × n1/2) mesh [PR]. This implies that in the presence of multiple buses, a skewed configuration may perform better than a square configuration for certain computational tasks. Our result can be extended to the J-dimensional mesh, giving a lower bound of ω(1/nd2d) and an upper bound of O(d2d+1 n 1/d2d).

Original language	English
Title of host publication	Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989
Editors	F.T. Leighton
Publisher	Association for Computing Machinery, Inc
Pages	138-147
Number of pages	10
ISBN (Electronic)	089791323X, 9780897913232
DOIs	https://doi.org/10.1145/72935.72951
State	Published - 1 Mar 1989
Externally published	Yes
Event	1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989 - Santa Fe, United States Duration: 18 Jun 1989 → 21 Jun 1989

Publication series

Name	Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989

Conference

Conference	1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989
Country/Territory	United States
City	Santa Fe
Period	18/06/89 → 21/06/89

Bibliographical note

Publisher Copyright:
© 1989 ACM.

Funding

*Computer Science Department, Stanford University, Stanford, CA 94305. Supported in part by a Weizmann fellowship and by contract ONR N00014-88-K-0166 l Department of Applied Mathematics, The Weizmann Institute, Rehovot 76100, Israel. Part of this work was carried out while this author was visiting Stanford university. Supported in part by a weizmarm fellowship, by contract ONR N00014-88-K-0166 and by a grant of Stanford Center for Integrated Systems.

Funders	Funder number
ONR N00014-88-K-0166 l Department of Applied Mathematics	ONR N00014-88-K-0166
Stanford Center for Integrated Systems

Access to Document

10.1145/72935.72951

Cite this

Bar-Noy, A., & Peleg, D. (1989). Square meshes are not always optimal. In F. T. Leighton (Ed.), Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989 (pp. 138-147). (Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989). Association for Computing Machinery, Inc. https://doi.org/10.1145/72935.72951

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title = "Square meshes are not always optimal",

abstract = "In this paper we consider mesh connected computers with multiple buses, providing broadcast facilities along rows and columns. A tight bound of 0(n?) is established for the number of rounds required for semigroup computations on n values distributed on a 2-dimensional rectangular mesh of size n with a bus on every row and column. The upper bound is obtained for a skewed rectangular mesh of dimensions n3/8 × n5/8 This result is to be contrasted with the tight bound of θ(n1/6) for the same problem on the square (n1/2 × n1/2) mesh [PR]. This implies that in the presence of multiple buses, a skewed configuration may perform better than a square configuration for certain computational tasks. Our result can be extended to the J-dimensional mesh, giving a lower bound of ω(1/nd2d) and an upper bound of O(d2d+1 n 1/d2d).",

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Bar-Noy, A & Peleg, D 1989, Square meshes are not always optimal. in FT Leighton (ed.), Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989. Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989, Association for Computing Machinery, Inc, pp. 138-147, 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989, Santa Fe, United States, 18/06/89. https://doi.org/10.1145/72935.72951

Square meshes are not always optimal. / Bar-Noy, Amotz; Peleg, David.
Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989. ed. / F.T. Leighton. Association for Computing Machinery, Inc, 1989. p. 138-147 (Proceedings of the 1st Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1989).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Square meshes are not always optimal

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