The Parallel Priority Queue (PPQ) data structure supports parallel operations for manipulating data items with keys, such as inserting n new items, deleting n items with the first n smallest keys, creating a new PPQ that contains a set of items, and melding two PPQ’s into one. In this paper, we present fast and efficient parallel algorithms for performing operations on the PPQ’s that maintain data items with real-valued keys. The data structures that we use for implementing the PPQ’s are the unmeldable and meldable parallel heaps. Our algorithms have considerably less time and/or work bounds than the previously best known algorithms, and use a less powerful parallel computational model (EREW PRAM). The new ideas that make our improvement possible are two partition schemes dynamically maintained on the parallel heap structures: the minimal- path partition and the right-path partition. These partition schemes could be of interest in their own right. Our results also lead to optimal parallel algorithms for implementing sequential operations on several commonly-used heap structures.
Parallel Algorithms for Constructing Range and Nearest-Neighbor Searching Data Structures
