Succinct representations of permutations

  • Authors:
  • J. Ian Munro;Rajeev Raman;Venkatesh Raman;Satti Srinivasa Rao

  • Affiliations:
  • School of Computer Science, Univ. of Waterloo, Waterloo, ON, Canada;Department of CS, Univ. of Leicester, Leicester, UK;Institute of Mathematical Sciences, Chennai, India;School of Computer Science, Univ. of Waterloo, Waterloo, ON, Canada

  • Venue:
  • ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
  • Year:
  • 2003

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Abstract

We investigate the problem of succinctly representing an arbitrary permutation, π, on {0, ..., n - 1} so that πk(i) can be computed quickly for any i and any (positive or negative integer) power k. A representation taking (1 + Ɛ)n lg n + O(1) bits suffices to compute arbitrary powers in constant time. A representation taking the optimal [lg n!] + o(n) bits can be used to compute arbitrary powers in O(lg n/lg lg n) time, or indeed in a minimal O(lg n) bit probes.