Multidimensional Costas Arrays and Their Enumeration Using GPUs and FPGAs

Rafael A. Arce-Nazario, Jose Ortiz-Ubarri
Department of Computer Science, University of Puerto Rico, Rio Piedras, San Juan, PR 00924, USA
International Journal of Reconfigurable Computing, Volume , Article ID 196761, 9 pages, 2012


   title={Multidimensional Costas Arrays and Their Enumeration Using GPUs and FPGAs},

   author={Arce-Nazario, R.A. and Ortiz-Ubarri, J.},

   journal={International Journal of Reconfigurable Computing},



   publisher={Hindawi Publishing Corporation}


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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 30x over the GPU (GeForce GTX 580).
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