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 Paper Abstract and Keywords Presentation 2012-03-16 10:35 A simple parallel computation algorithm for functions on treesKunihiko 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 Keyword(4) Keyword(5) Keyword(6) Keyword(7) Keyword(8) 1st Author's Name Kunihiko Sadakane 1st Author's Affiliation National Institute of Informatics (NII) 2nd Author's Name 2nd Author's Affiliation () 3rd Author's Name 3rd Author's Affiliation () 4th Author's Name 4th Author's Affiliation () 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 1 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