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Paper Abstract and Keywords
Presentation 2012-03-16 10:35
A simple parallel computation algorithm for functions on trees
Kunihiko Sadakane (NII)
Abstract (in Japanese) (See Japanese page) 
(in English) We propose a simple parallel algorithm for computing a function defined on a
rooted tree with $n$ nodes. Namely, we want to compute the value of a function $f(r)$ for the root node $r$, defined as
$f(v) = w(v) \otimes \left(\bigoplus_{u \in S(v)} f(u) \right)$
where $S(v)$ denotes the set of child nodes of the node $v$.
We propose a simple EREW-PRAM algorithm for computing the function
in $\Order(n/p + \log^2 p)$ time using $p$ processors.
We assume that the operators $\otimes$ and $\oplus$ satisfy the following:
$\otimes$ is associative, left-distributive over $\oplus$, and
$\oplus$ is associative.
If $\otimes$ has the inverse (i.e., $\otimes$ forms a group),
the time complexity is improved to $\Order(n/p + \log p)$.
Our algorithm is space efficient. If the weight of a node is represented in $k$ bits and the value of the function
is represented in $W$ bits, our algorithm uses $2(k+1)n$ bits to store the tree, and uses
$\Order(p(W+\log n))$ bit working space for computing the function.
Because of the simplicity and space-efficiency,
the algorithm is suitable for GPGPU.
Keyword (in Japanese) (See Japanese page) 
(in English) tree functions / EREW-PRAM / GPGPU / / / / /  
Reference Info. IEICE Tech. Rep., vol. 111, no. 494, COMP2011-48, pp. 9-15, March 2012.
Paper # COMP2011-48 
Date of Issue 2012-03-09 (COMP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380

Conference Information
Committee COMP  
Conference Date 2012-03-16 - 2012-03-16 
Place (in Japanese) (See Japanese page) 
Place (in English) Univ. of Tokyo 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2012-03-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A simple parallel computation algorithm for functions on trees 
Sub Title (in English)  
Keyword(1) tree functions  
Keyword(2) EREW-PRAM  
Keyword(3) GPGPU  
1st Author's Name Kunihiko Sadakane  
1st Author's Affiliation National Institute of Informatics (NII)
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Date Time 2012-03-16 10:35:00 
Presentation Time 20 
Registration for COMP 
Paper # IEICE-COMP2011-48 
Volume (vol) IEICE-111 
Number (no) no.494 
Page pp.9-15 
#Pages IEICE-7 
Date of Issue IEICE-COMP-2012-03-09 

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