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In this paper we focus on the problem of designing very fast parallel algorithms for the convex hull and the vector maxima problems in three dimensions that are output-size sensitive. Our algorithms achieve Oðlog log 2 n log hÞ parallel time and optimal Oðn log hÞ work with high probability in the CRCW PRAM where n and h are the input and output size, respectively. These bounds are independent of the input distribution and are faster than the previously known algorithms. We also present andoi:10.1016/s0743-7315(03)00035-2 fatcat:l27fsx5wb5alzhl2bv3lmgatdm