Research Note
O(log logN) Time Algorithms for Hamiltonian Suffix and Min-Max-Pair Heap Operations on the Hypercube

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Abstract

This paper deals with a fast implementation of a heap data structure on a hypercube-connected, synchronous, distributed-memory multicomputer. In particular, we present a communication-efficient mapping of a min-max-pair heap on the hypercube architecture in which the load on each processor's local memory is balanced and propose cost-optimal parallel algorithms which requireO((logN)/p+ logp) time to perform single insertion, deletemin, and deletemax operations on a min-max-pair heap of sizeN, wherepis the number of processors. Our implementation is based on an embedding of complete binary trees in the hypercube and an efficient parallel solution to a special kind of suffix computation, that we call theHamiltonian suffix, along a Hamiltonian path in the hypercube. The binary tree underlying the heap data structure is, however, not altered by the mapping process.

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This work is partially supported by a Texas Advanced Technology Program grant under Award TATP-003594031. The authors can be reached via e-mail at [email protected] and [email protected].

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