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Raising Permutations to Powers in Place

Authors Hicham El-Zein, J. Ian Munro, Matthew Robertson

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Hicham El-Zein
J. Ian Munro
Matthew Robertson

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Hicham El-Zein, J. Ian Munro, and Matthew Robertson. Raising Permutations to Powers in Place. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 29:1-29:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ISAAC.2016.29

Abstract

Given a permutation of n elements, stored as an array, we address the problem of replacing the permutation by its kth power. We aim to perform this operation quickly using o(n) bits of extra storage. To this end, we first present an algorithm for inverting permutations that uses O(lg^2 n) additional bits and runs in O(n lg n) worst case time. This result is then generalized to the situation in which the permutation is to be replaced by its kth power. An algorithm whose worst case running time is O(n lg n) and uses O(lg^2 n + min{k lg n, n^{3/4 + epsilon}}) additional bits is presented.
Keywords
  • Algorithms
  • Combinatorics
  • Inplace
  • Permutations
  • Powers

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