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The asymptotic complexity of merging networks
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Miltersen, Peter Bro, Paterson, Michael S. and Tarui, Jun (1996) The asymptotic complexity of merging networks. Journal of the ACM, Volume 43 (Number 1). pp. 147-165. ISSN 0004-5411.
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Official URL: http://dx.doi.org/10.1145/227595.227693
Abstract
Let M(m, n) be the minimum number of comparators needed in a comparator network that merges m elements x(1) less than or equal to x(2) less than or equal to ... less than or equal to x(m) and n elements y(1) less than or equal to y(2) less than or equal to ... less than or equal to y(n), where n greater than or equal to m. Batcher's odd-even merge yields the following upper bound:
M(m,n) less than or equal to 1/2(m + n)log(2)m + O(n);
in particular,
M(n,n) less than or equal to n log(2)n + O(n).
We prove the following lower bound that matches the upper bound above asymptotically as n greater than or equal to m --> infinity:
M(m,n) greater than or equal to 1/2(m + n)log(2)m - O(m);
in particular,
M(n,n) greater than or equal to 1/2 n log(2)n - O(n).
Our proof technique extends to give similarly tight Lower bounds for the size of monotone Boolean circuits for merging, and for the size of switching networks capable of realizing the set of permutations that arise from merging.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Journal or Publication Title: | Journal of the ACM | ||||
| Publisher: | Association for Computing Machinery, Inc. | ||||
| ISSN: | 0004-5411 | ||||
| Official Date: | January 1996 | ||||
| Dates: |
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| Volume: | Volume 43 | ||||
| Number: | Number 1 | ||||
| Number of Pages: | 19 | ||||
| Page Range: | pp. 147-165 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Version or Related Resource: | Miltersen, P.B., Paterson, M.S. and Tarui, J. (1995). The asymptotic complexity of merging networks. University of Warwick. Department of Computer Science. (Department of Computer Science research report, 216) | ||||
| Related URLs: |
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