Parallel and distributed meldable priority queues based on binomial heaps

On the parallel random access machine (PRAM) models, we present an optimal implementation of a meldable priority queue based on the binomial heap data structure. Doubly logarithmic time, cost-optimal algorithms are proposed on the EREW PRAM model for such queue-operations as Insert, Min, Extract-Min, and Union (often called melding). Our Union algorithm exploits its natural similarity with the problem of adding two binary integers. Two other operations, Change-Key and Delete, are also solved optimally on the CREW PRAM model and their amortized complexity is analyzed. The algorithm for Delete operation uses tricks for postponing the global effect of a node deletion. Additionally, we present an implementation of a distributed meldable priority queue on, the single-port hypercube model. Adopting a b-bandwidth binomial heap as the underlying data structure and a mapping which minimizes the amount of data movement among the processors when two binomial trees are melded, the hypercube algorithm, attains a nearly optimal amortized speed-up for the Insert, Extract-Min and Union operations