Deriving a Fast Inverse of the Generalized Cantor N-tupling Bijection

Author Paul Tarau



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Paul Tarau

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Paul Tarau. Deriving a Fast Inverse of the Generalized Cantor N-tupling Bijection. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 17, pp. 312-322, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.ICLP.2012.312

Abstract

We attack an interesting open problem (an efficient algorithm to invert the generalized Cantor N-tupling bijection) and solve it through a sequence of equivalence preserving transformations of logic programs, that take advantage of unique strengths of this programming paradigm. An extension to set and multiset tuple encodings, as well as a simple application to a "fair-search" mechanism illustrate practical uses of our algorithms. The code in the paper (a literate Prolog program, tested with SWI-Prolog and Lean Prolog) is available at http://logic.cse.unt.edu/tarau/research/2012/pcantor.pl .
Keywords
  • generalized Cantor n-tupling bijection
  • bijective data type transformations
  • combinatorial number system
  • solving combinatorial problems in Prolog
  • op

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