Tries-Based Parallel Solutions for Generating Perfect Crosswords Grids

Abstract

A general crossword grid generation is considered an NP-complete problem and theoretically it could be a good candidate to be used by cryptography algorithms. In this article, we propose a new algorithm for generating perfect crosswords grids (with no black boxes) that relies on using tries data structures, which are very important for reducing the time for finding the solutions, and offers good opportunity for parallelisation, too. The algorithm uses a special tries representation and it is very efficient, but through parallelisation the performance is improved to a level that allows the solution to be obtained extremely fast. The experiments were conducted using a dictionary of almost 700,000 words, and the solutions were obtained using the parallelised version with an execution time in the order of minutes. We demonstrate here that finding a perfect crossword grid could be solved faster than has been estimated before, if we use tries as supporting data structures together with parallelisation. Still, if the size of the dictionary is increased by a lot (e.g., considering a set of dictionaries for different languages—not only for one), or through a generalisation to a 3D space or multidimensional spaces, then the problem still could be investigated for a possible usage in cryptography.

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