Parallel algorithms for tree accumulations

Accumulations are abstract operations on trees useful in many applications involving trees. The upward accumulation problem is to aggregate data in the subtree under each node of the tree. The downward accumulation problem is to aggregate data at all the ancestors of each node. In this paper, we pre...

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Published in	Journal of parallel and distributed computing Vol. 65; no. 1; pp. 85 - 93
Main Authors	Sevilgen, Fatih E., Aluru, Srinivas, Futamura, Natsuhiko
Format	Journal Article
Language	English
Published	San Diego, CA Elsevier Inc 2005 Elsevier
Subjects	Applied sciences Computer science; control theory; systems Downward accumulation Exact sciences and technology Memory and file management (including protection and security) Memory organisation. Data processing Parallel prefix Software Tree contraction Upward accumulation Tree contraction Downward accumulation Parallel prefix Upward accumulation Distributed memory Parallel algorithm Parallel computer Synchronization
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ISSN	0743-7315 1096-0848
DOI	10.1016/j.jpdc.2004.09.001

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Abstract	Accumulations are abstract operations on trees useful in many applications involving trees. The upward accumulation problem is to aggregate data in the subtree under each node of the tree. The downward accumulation problem is to aggregate data at all the ancestors of each node. In this paper, we present parallel algorithms for these problems on coarse-grained distributed memory parallel computers. We first show that when the accumulation function and the set of possible values at nodes of the tree form an Abelian (commutative) group, this problem can be solved by a remarkably simple algorithm—Upward accumulation takes O n p + τ p + μ n p time, where n is the number of nodes in the tree, p is the number of processors, τ is the communication latency and μ is the transfer time per unit message size. Downward accumulation takes O n p + ( τ + μ ) log p time, making it very communication efficient. For the general case, we present upward and downward accumulation algorithms that run in O n p log n + τ p log n + μ n p log n time.
AbstractList	Accumulations are abstract operations on trees useful in many applications involving trees. The upward accumulation problem is to aggregate data in the subtree under each node of the tree. The downward accumulation problem is to aggregate data at all the ancestors of each node. In this paper, we present parallel algorithms for these problems on coarse-grained distributed memory parallel computers. We first show that when the accumulation function and the set of possible values at nodes of the tree form an Abelian (commutative) group, this problem can be solved by a remarkably simple algorithm—Upward accumulation takes O n p + τ p + μ n p time, where n is the number of nodes in the tree, p is the number of processors, τ is the communication latency and μ is the transfer time per unit message size. Downward accumulation takes O n p + ( τ + μ ) log p time, making it very communication efficient. For the general case, we present upward and downward accumulation algorithms that run in O n p log n + τ p log n + μ n p log n time.
Author	Aluru, Srinivas Futamura, Natsuhiko Sevilgen, Fatih E.
Author_xml	– sequence: 1 givenname: Fatih E. surname: Sevilgen fullname: Sevilgen, Fatih E. email: sevilgen@bilmuh.gyte.edu.tr organization: Computer Engineering, Gebze Institute of Technology, Turkey – sequence: 2 givenname: Srinivas surname: Aluru fullname: Aluru, Srinivas email: aluru@iastate.edu organization: Department of Electrical and Computer Engineering, Iowa State University, 3218 Coover Hall, Ames, IA 50011, USA – sequence: 3 givenname: Natsuhiko surname: Futamura fullname: Futamura, Natsuhiko email: nfutamur@cs.wright.edu organization: Computer Science and Engineering, Wright State University, Dayton, OH 45435, USA
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Keywords	Tree contraction Downward accumulation Parallel prefix Upward accumulation Distributed memory Parallel algorithm Parallel computer Synchronization
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