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A fast GPU-based hybrid algorithm for addition chains

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Abstract

A graphics processing unit (GPU) has been widely used to accelerate discrete optimization problems. In this paper, we introduce a novel hybrid parallel algorithm to generate a shortest addition chain for a positive integer e. The main idea of the proposed algorithm is to divide the search tree into a sequence of three subtrees: top, middle, and bottom. The top subtree works using a branch and bound depth first strategy. The middle subtree works using a branch and bound breadth first strategy, while the bottom subtree works using a parallel (GPU) branch and bound depth first strategy. Our experimental results show that, compared to the fastest sequential algorithm for generating a shortest addition chain, we improve the generation by about 70% using one GPU (NVIDIA GeForce GTX 770). For generating all shortest addition chains, the percentage of the improvement is about 50%.

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Authors and Affiliations

  1. Computer Science Division, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, 11566, Egypt

    Hatem M. Bahig & Khaled A. AbdElbari

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  1. Hatem M. Bahig
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  2. Khaled A. AbdElbari
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Correspondence to Hatem M. Bahig.

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Bahig, H.M., AbdElbari, K.A. A fast GPU-based hybrid algorithm for addition chains. Cluster Comput 21, 2001–2011 (2018). https://doi.org/10.1007/s10586-018-2840-5

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