On computing the length of longest increasing subsequences

Abstract

Let S = x₁, x₂, … x_n be a sequence of n distinct elements from a linearly ordered set. We consider the problem of determining the length of the longest increasing subsequences of S. An algorithm which performs this task is described and is shown to perform n log n−n log log n + O(n) comparisons in its worst case. This worst case behavior is shown to be best possible.