In this paper we present a new randomized selection algorithm on the Bulk-Synchronous Parallel (BSP) model of computation along with an application of this algorithm to dynamic data structures, namely Parallel Priority Queues (PPQs). We show that our algorithms improve previous results upon both the communication requirements and the amount of parallel slack required to achieve optimal performance. We also establish that optimality to within small multiplicative constant factors can be achieved for a wide range of parallel machines. While these algorithms are fairly simple themselves, descriptions of their performance in terms of the BSP parameters is somewhat involved. The main reward of quantifying these complications is that it allows transportable software to be written for parallel machines that fit the model. We also present experimental results for the selection algorithm that reinforce our claims
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