Path Finding and Pattern Spotting in Toroidal Topologies: A Study on de Bruijn Structures, k-ary n-Cubes, and Toroidal k-ary Grids
Pedro J. Roig *
Miguel Hernández University, Elche, Spain and University of the Balearic Islands, Spain.
Salvador Alcaraz
Miguel Hernández University, Elche, Spain.
Katja Gilly
Miguel Hernández University, Elche, Spain.
Cristina Bernad
Miguel Hernández University, Elche, Spain.
Carlos Juiz
University of the Balearic Islands, Spain.
*Author to whom correspondence should be addressed.
Abstract
This paper examines toroidal layouts with a focus on their roles in pattern spotting and path-finding strategies. While de Bruijn structures provide a precise method to locate specific patterns, k-ary n-cubes and toroidal k-ary grids enable efficient path finding through different node organization principles. The study compares these structures by modeling their underlying strategies and presenting algorithmic solutions in pseudocode. The results highlight the complementary strengths of each approach, offering useful insights for applications in network routing, parallel computing, and data organization.
Keywords: Toroidal topologies, de bruijn structures, k-ary n-cubes, toroidal k-ary grids, topology