Combinatorics of patience sorting monoids

Enumerating Longest Increasing Subsequences and Patience Sorting Enumerating Longest Increasing Subsequences and Patience Sorting

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 en...

Enumerating longest increasing subsequences and patience sorting

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 en...

A Cost Optimal Parallel Algorithm for Patience Sorting

A Theory of Transformation Monoids: Combinatorics and Representation Theory

The aim of this paper is to develop a theory of finite transformation monoids and in particular to study primitive transformation monoids. We introduce the notion of orbitals and orbital digraphs for transformation monoids and prove a monoid version of D. Higman’s celebrated theorem characterizing primitivity in terms of connectedness of orbital digraphs. A thorough study of the module (or repr...

Parallel Algorithms for Patience Sorting and Longest Increasing Subsequence

In this paper, we consider parallel algorithms for the patience sorting and the longest increasing subsequence. These two problems are related each other and are not known to be in the class NC or P -complete. We first propose two algorithms for the patience sorting of n distinct integers. The first algorithm runs in O(m(np + logn)) time using p processors on the EREW PRAM, where m is the numbe...