Sorting with a forklift

TL;DR

This paper investigates the capabilities of a generalized stack structure called a fork stack, providing algorithms to determine sortable sequences, identifying minimal unsortable sequences, and extending results to bounded push/pop operations.

Contribution

It introduces algorithms for sorting with fork stacks, characterizes minimal unsortable sequences, and extends the analysis to bounded push/pop operations.

Findings

Provided an algorithm to determine sortable sequences.

Identified minimal unsortable sequences.

Extended results to bounded push and pop operations.

Abstract

A fork stack is a generalised stack which allows pushes and pops of several items at a time. We consider the problem of determining which input streams can be sorted using a single forkstack, or dually, which permutations of a fixed input stream can be produced using a single forkstack. An algorithm is given to solve the sorting problem and the minimal unsortable sequences are found. The results are extended to fork stacks where there are bounds on how many items can be pushed and popped at one time. In this context we also establish how to enumerate the collection of sortable sequences.