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A new strategy for generating shortest addition sequences

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Abstract

An addition sequence problem is given a set of numbers X = {n 1, n 2, . . . , n m }, what is the minimal number of additions needed to compute all m numbers starting from 1? This problem is NP-complete. In this paper, we present a branch and bound algorithm to generate an addition sequence with a minimal number of elements for a set X by using a new strategy. Then we improve the generation by generalizing some results on addition chains (m = 1) to addition sequences and finding what we will call a presumed upper bound for each n j , 1 ≤ j ≤ m, in the search tree.

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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 & Hazem M. Bahig

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  1. Hatem M. Bahig
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  2. Hazem M. Bahig
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Correspondence to Hatem M. Bahig.

Additional information

Communicated by F. Rendl.

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Bahig, H.M., Bahig, H.M. A new strategy for generating shortest addition sequences. Computing 91, 285–306 (2011). https://doi.org/10.1007/s00607-010-0119-7

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  • DOI: https://doi.org/10.1007/s00607-010-0119-7

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