Valid Orderings of Layers When Simple-Folding a Map

Abstract

In this work, we consider a decision problem on whether an overlapping order of all the squares of an m × n map is valid under a particular context called simple folding. This problem belongs to the field of map folding. It is a variation of both the decision problem of valid orders of a 1 × n map under the context of simple folds and the decision problem of valid orders of an m × n map under the context of general folds. We provide a method and its corresponding linear-time algorithm to solve this problem, which is based on the construction of a directed graph representing the adjacency relations among squares.