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Computers 2019, 8(1), 23; https://doi.org/10.3390/computers8010023

An Efficient Multicore Algorithm for Minimal Length Addition Chains

1,2 and 2,3,*
1
College of Computer Science and Engineering, Hail University, Hail 81481, Kingdom of Saudi Arabia
2
Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
3
College of Computer and Information Sciences, Information Systems Department, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Kingdom of Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 11 December 2018 / Revised: 12 February 2019 / Accepted: 4 March 2019 / Published: 7 March 2019
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Abstract

A minimal length addition chain for a positive integer m is a finite sequence of positive integers such that (1) the first and last elements in the sequence are 1 and m, respectively, (2) any element greater than 1 in the sequence is the addition of two earlier elements (not necessarily distinct), and (3) the length of the sequence is minimal. Generating the minimal length addition chain for m is challenging due to the running time, which increases with the size of m and particularly with the number of 1s in the binary representation of m. In this paper, we introduce a new parallel algorithm to find the minimal length addition chain for m. The experimental studies on multicore systems show that the running time of the proposed algorithm is faster than the sequential algorithm. Moreover, the maximum speedup obtained by the proposed algorithm is 2.5 times the best known sequential algorithm. View Full-Text
Keywords: addition chain; minimal length; parallel algorithm; branch-and-bound; multicore; high performance computing addition chain; minimal length; parallel algorithm; branch-and-bound; multicore; high performance computing
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Bahig, H.M.; Kotb, Y. An Efficient Multicore Algorithm for Minimal Length Addition Chains. Computers 2019, 8, 23.

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