Abstract
We study parallel solutions to the problem of implementing priority queues and priority deques. It is known that data structures for the implementation (e.g., the heap, the minmax heap, and the deap) can be constructed in linear sequential time. In this paper, we design optimal Ω((log log n)2) time parallel algorithms with n/(log logn)2 processors for the constructions on the parallel comparison tree model. For building heaps in parallel, our algorithm improves the previous best result of Ω(log n) time with n/log n processors. For building min-max heaps and deaps, our algorithms are the first attempt to design parallel algorithms for constructing the data structures of the priority deque that are cost optimal.
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