Abstract
In this paper we give improved bounds for the multisearch problem on a hypercube. This is a parallel search problem where the elements in the structure S to be searched are totally ordered, but where it is not possible to compare in constant time any two given queries q and q′. This problem is fundamental in computational geometry, for example it models planar point location in a slab. More precisely, we are given on a n-processor hypercube a sorted n-element sequence S, and a set Q of n queries, and we need to find for each query q ε Q its location in the sorted S. Note that one cannot solve this problem by sorting S ∪ Q, because every comparison-based parallel sorting algorithm needs to compare a pair q,q′ ε Q in constant time. We present an improved algorithm for the multisearch problem, one that takes O(log n(log log n)3) time on a n- processor hypercube. This essentially replaces a logarithmic factor in the time complexities of previous schemes by a (log log n)3 factor. The hypercube model for which we claim our bounds is the standard one, SIMD, with O(1) memory registers per processor, and with one-port communication. Each register can store O(log n) bits, so that a processor knows its ID.
This work was supported in part by the National Science. Foundation under Grant CCR9202807, and by the ESPRIT Basic Research Action Nr. 7141 (ALCOM II).
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References
K.E. Batcher. Sorting networks and their applications. Proc. AFIPS Spring Joint Computer Conference, pp. 307–314, 1968.
R. Cypher, C.G. Plaxton. Deterministic Sorting in Nearly Logarithmic Time on the Hypercube and Related Computers. ACM Proceedings of the 22th Annual ACM Symposium on Theory of Computing, pp. 193–203, 1990.
F. Dehne, A. Rau-Chaplin. Implementing Data Structures on a Hypercube Multiprocessor, and Applications in Parallel Computational Geometry, J. Parallel Distrib. Computing, Vol. 8, 1990, pp. 367–375.
F. Dehne, A. Ferreira, A. Rau-Chaplin. Parallel fractional cascading on hypercube multiprocessors. Computational Geometry: Theory and Applications 2, pp. 141–167, 1992.
D. T. Lee, F. P. Preparata. Parallel Batched Planar Poin Location on the CCC, Information Processing Letters, 33, pp. 175–179, 1989.
F. T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufmann Publishers, San Mateo, CA, 1992.
D. Nassimi and S. Sahni. Data broadcasting in SIMD computers. IEEE Transactions on Computers, C-30(2):101–107, February 1981.
J.H. Reif, S. Sen. Randomized Algorithms for Binary Search and Load Balancing on Fixed Connection Networks with Geometric Applications. Proceedings of the 2nd Annual Symposium on Parallel Algorithms and Architectures, 1990.
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© 1994 Springer-Verlag Berlin Heidelberg
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Atallah, M.J., Fabri, A. (1994). On the multisearching problem for hypercubes. In: Halatsis, C., Maritsas, D., Philokyprou, G., Theodoridis, S. (eds) PARLE'94 Parallel Architectures and Languages Europe. PARLE 1994. Lecture Notes in Computer Science, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58184-7_98
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DOI: https://doi.org/10.1007/3-540-58184-7_98
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