On the longest increasing subsequence of a circular list

  • Authors:
  • M. H. Albert;M. D. Atkinson;Doron Nussbaum;Jörg-Rüdiger Sack;Nicola Santoro

  • Affiliations:
  • Department of Computer Science, University of Otago, Dunedin, New Zealand;Department of Computer Science, University of Otago, Dunedin, New Zealand;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S5B6, Canada;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S5B6, Canada;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S5B6, Canada

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

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Abstract

The longest increasing circular subsequence (LICS) of a list is considered. A Monte Carlo algorithm to compute it is given which has worst case execution time O(n^3^/^2logn) and storage requirement O(n). It is proved that the expected length @m(n) of the LICS satisfies lim"n"-"~@m(n)2n=1. Numerical experiments with the algorithm suggest that |@m(n)-2n|=O(n^1^/^6).