) Ajay K. Gupta ? Andreas G. Photiou Western Michigan University Lake States Insurance Company Kalamazoo, MI 49008, USA Traverse City, MI 49685, USA Abstract. We consider efficient algorithms for priority queues on distributed memory multiprocessors, such as nCUBE, iPSc, MPP and looselycoupled systems consisting of networked workstations. For a p-processor distributed memory multicomputer P and n data items in the priority queue, n ? p, we investigate two priority queues; horizontally sliced and vertically sliced. Both of these achieve load balance, i.e. at most \Theta(n=p) data items are stored at every processor of P . Horizontally sliced priority queue allows deletions and insertions of \Theta(p) items in time O( p bw øc + øpp log n) on hypercubic networks where øc is the communication time between a pair of processors, øp is the unit processing time and bw is the width of the communication channel between a pair of processors. Vertically sliced priority queue allows deletio...