, Volume 91, Issue 3, pp 285–306 | Cite as

A new strategy for generating shortest addition sequences



An addition sequence problem is given a set of numbers X = {n1, n2, . . . , nm}, 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 nj, 1 ≤ j ≤ m, in the search tree.


Addition chains Addition sequences Branch and bound algorithm High-performance arithmetic Monomials evaluation Vectorial addition chains 

Mathematics Subject Classification (2000)

68W01 68T20 11Y55 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Computer Science Division, Department of Mathematics, Faculty of ScienceAin Shams UniversityCairoEgypt

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