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Computing

, Volume 63, Issue 4, pp 341–349 | Cite as

Minimal Expansions in Redundant Number Systems and Shortest Paths in Graphs

  • C. Heuberger
Article
  • 31 Downloads

Abstract.

We consider digit expansions \(n=\sum_{i=0}^l \epsilon_iq^i\) in redundant number systems to base q with \(-(q-1)\le \epsilon_i\le q-1\) and consider such an expansion as minimal, if \(l + \sum\nolimits_{i = 0}^l {|\varepsilon _i |} \) is minimal. We describe an efficient algorithm for determining a minimal representation and give an explicit characterization of optimal representations for odd q.

AMS Subject Classifications:11A63, 05C12, 68R10. 
Key words.Radix expansion, redundant number systems, shortest paths in graphs. 

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Copyright information

© Springer Verlag, Wien 1999

Authors and Affiliations

  • C. Heuberger
    • 1
  1. 1.Institut für Mathematik B, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria, e-mail:cheub@weyl.math.tu-graz.ac.at AT

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