Heaps with bits

Abstract

In this paper, we show how to improve the complexity of heap operations and heapsort using extra bits. We first study parallel complexity of implementing priority queue operations on a heap. While the insertion of a new element into a heap can be done as fast as parallel searching, we show how to delete the smallest element from a heap in constant time with a sublinear number of processors, and in sublogarithmic time with a sublogarithmic number of processors. The models of parallel computation used are the CREW PRAM and the CRCW PRAM. Our results improve those of previously known algorithms. Moreover, we study a variant, fine-heap, of the traditional heap structure. A fast algorithm for constructing this new data structure is designed, which is also used to develop an improved heapsort algorithm. Our variation of heapsort is faster than McDiarmid and Reed’s variant of heapsort and requires less extra space.