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The advent of multicore and many-core architectures saw them being deployed to speed-up computations across several disciplines and application areas. Prominent examples include semi-numerical algorithms such as sorting, graph algorithms, image processing, scientific computations, and the like. In particular, using GPUs for general purpose computations has attracted a lot of attention given that GPUs can deliver more than one TFLOP of computing power at very low prices. In this work, we use a new model of multicore computing called hybrid multicore computing where the computation is performed simultaneously a control device, such as a CPU, and an accelerator such as a GPU. To this end, we use two case studies to explore the algorithmic and analytical issues in hybrid multicore computing. Our case studies involve two different ways of designing hybrid multicore algorithms. The main contribution of this paper is to address the issues related to the design of hybrid solutions. We show our hybrid algorithm for list ranking is faster by 50% compared to the best known implementation [Z. Wei, J. JaJa; IPDPS 2010]. Similarly, our hybrid algorithm for graph connected components is faster by 25% compared to the best known GPU implementation .