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International Journal of Reconfigurable Computing
Volume 2012 (2012), Article ID 196761, 9 pages
Research Article

Multidimensional Costas Arrays and Their Enumeration Using GPUs and FPGAs

Department of Computer Science, University of Puerto Rico, Río Piedras, San Juan, PR 00924, USA

Received 4 May 2012; Accepted 17 September 2012

Academic Editor: René Cumplido

Copyright © 2012 Rafael A. Arce-Nazario and José Ortiz-Ubarri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The enumeration of two-dimensional Costas arrays is a problem with factorial time complexity and has been solved for sizes up to 29 using computer clusters. Costas arrays of higher dimensionality have recently been proposed and their properties are beginning to be understood. This paper presents, to the best of our knowledge, the first proposed implementations for enumerating these multidimensional arrays in GPUs and FPGAs, as well as the first discussion of techniques to prune the search space and reduce enumeration run time. Both GPU and FPGA implementations rely on Costas array symmetries to reduce the search space and perform concurrent explorations over the remaining candidate solutions. The fine grained parallelism utilized to evaluate and progress the exploration, coupled with the additional concurrency provided by the multiple instanced cores, allowed the FPGA (XC5VLX330-2) implementation to achieve speedups of up to 30× over the GPU (GeForce GTX 580).