On the longest increasing subsequence of a circular list

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 (n3 / 2 log n) and storage requirement O (n). It is proved that the expected length μ (n) of the LICS satisfies limn → ∞ frac(μ (n), 2 sqrt(n)) = 1. Numerical experiments with the algorithm suggest that | μ (n) - 2 sqrt(n) | = O (n1 / 6). © 2006 Elsevier B.V. All rights reserved.