Enumerating longest increasing subsequences and patience sorting

Abstract

In this paper we present three algorithms that solve three combinatorial optimization problems related to each other. One of them is the patience sorting game, invented as a practical method of sorting real decks of cards. The second problem is computing the longest monotone increasing subsequence of the given sequence of n positive integers in the range 1,…,n. The third problem is to enumerate all the longest monotone increasing subsequences of the given permutation.