The periodic balanced sorting network
Journal of the ACM (JACM)
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Comparator networks for binary heap construction
Theoretical Computer Science
Communications of the ACM
Periodic, random-fault-tolerant correction networks
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Optimal Parallel Initialization Algorithms for a Class of Priority Queues
IEEE Transactions on Parallel and Distributed Systems
Heap Construction in the Parallel Comparison Tree Model
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A Flexible Reservation Algorithm for Advance Network Provisioning
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
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We consider the problem of constructing binary heaps on constant degree networks performing compare-exchange operations only. The heap data structure, introduced by William and Williams [Comm. ACM 7 (6) (1964) 347-348], has many applications and, therefore, has been intensively studied in sequential and parallel context. In particular, Brodal and Pinotti [Theoret. Comput. Sci. 250 (2001) 235-245] have recently presented two families of comparator networks: the first of depth 4 log N and the second of size O(N log log N) for constructing binary heaps of size N. In this note, we give an new construction of such a network with the running time improved to 3 log N. Moreover, the network has a novel property of being 3-periodic, that is, for each unit of time i the same sets of operations are performed in units i and i + 3. Then we argue that our construction is optimal with respect to the length of the period, that is, we prove that there is no 2-periodic network that is able to build a binary heap in sublinear time. Finally, we show that our construction can be used to decrease also the depth of the networks with O(N log log N) size.