Abstract
We give an improved parallel algorithm for the problem of computing the tube minima of a totally monotone n × n × n matrix, an important matrix searching problem that was formalized by Aggarwal and Park and has many applications. Our algorithm runs in O(log log n) time with O(n 2/log log n) processors in the CRCW-PRAM model, whereas the previous best ran in O((log log n)2) time with O(n 2/(log log n)2) processors, also in the CRCW-PRAM model. Thus we improve the speed without any deterioration in the time × processors product. Our improved bound immediately translates into improved CRCW-PRAM bounds for the numerous applications of this problem, including string editing, construction of Huffmann codes and other coding trees, and many other combinatorial and geometric problems.
This research was supported by the Office of Naval Research under Grants N00014-84-K-0502 and N00014-86-K-0689, the National Science Foundation under Grant DCR-8451393, and the National Library of Medicine under Grant R01-LM05118. Part of the research was done while the author was at Princeton University, visiting the DIMACS center.
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References
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© 1990 Springer-Verlag Berlin Heidelberg
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Atallah, M.J. (1990). A faster parallel algorithm for a matrix searching problem. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_89
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DOI: https://doi.org/10.1007/3-540-52846-6_89
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