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We propose a design for a fine-grained lock-based skiplist optimized for Graphics Processing Units (GPUs). While GPUs are often used to accelerate streaming parallel computations, it remains a significant challenge to efficiently offload concurrent computations with more complicated data-irregular access and fine-grained synchronization. Natural building blocks for such computations would be concurrent data structures, such as skiplists, which are widely used in general purpose computations. Our design utilizes array-based nodes which are accessed and updated by warp-cooperative functions, thus taking advantage of the fact that GPUs are most efficient when memory accesses are coalesced and execution divergence is minimized. The proposed design has been implemented, and measurements demonstrate improved performance of up to 11.6x over skiplist designs for the GPU existing today.