Parallel Algorithms for Priority Queue Operations

This paper presents parallel algorithms for priority queue operations on a p-processor EREW-PRAM. The algorithms are based on a new data structure, the Min-path Heap (MH), which is obtained as an extension of the traditional binary-heap organization. Using an MH, it is shown that insertion of a new item or deletion of the smallest item from a priority queue of n elements can be performed in O(log n p + log log n) parallel time, while construction of an MH from a set of n items takes O(n p + log n) time. The given algorithms for insertion and deletion achieve the best possible running time for any number of processors p, with p 2 O(log n log log n), while the MH construction algorithm employs up to (n log n) processors optimally. The paper ends with a brief discussion of the applicability of MH's to the development of eecient parallel algorithms for some important combinatorial problems.