The k-mers processing techniques based on partitioning of the data set on the disk using minimizer-type seeds have led to a significant reduction in memory requirements; however, it has added processes (search and distribution of super k-mers) that can be intensive given the large volume of data. This paper presents a massive parallel processing model in order to enable the efficient use of heterogeneous computation to accelerate the search of super k-mers based on seeds (minimizers or signatures). The model includes three main contributions: a new data structure called CISK for representing the super k-mers, their minimizers and two massive parallelization patterns in an indexed and compact way: one for obtaining the canonical m-mers of a set of reads and another for searching for super k-mers based on minimizers. The model was implemented through two OpenCL kernels. The evaluation of the kernels shows favorable results in terms of execution times and memory requirements to use the model for constructing heterogeneous solutions with simultaneous execution (workload distribution), which perform co-processing using the current search methods of super k -mers on the CPU and the methods presented herein on GPU. The model implementation code is available in the repository: https://github.com/BioinfUD/K-mersCL.