## Efficient Parallel Algorithms for Tree Accumulations (1994)

Venue: | Science of Computer Programming |

Citations: | 19 - 7 self |

### BibTeX

@ARTICLE{Gibbons94efficientparallel,

author = {Jeremy Gibbons and Wentong Cai and David B. Skillicorn},

title = {Efficient Parallel Algorithms for Tree Accumulations},

journal = {Science of Computer Programming},

year = {1994},

volume = {23},

pages = {1--18}

}

### Years of Citing Articles

### OpenURL

### Abstract

Accumulations are higher-order operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree algorithms. We present two Erew Pram algorithms for computing accumulations on trees taking O(log n) time on O(n= log n) processors, which is optimal.

### Citations

290 | Parallel prefix computation
- Ladner, Fischer
- 1980
(Show Context)
Citation Context ...). Accepted for publication in Science of Computer Programming. Efficient parallel algorithms for tree accumulations 2 upwards and downwards accumulation, respectively. The parallel prefix algorithm (=-=Ladner and Fischer, 1980-=-) for computing the prefix sums of a list in logarithmic time on linearly many processors involves building a tree with the list elements as leaves, then performing an upwards and downwards accumulati... |

253 | The parallel evaluation of general arithmetic expressions
- Brent
- 1974
(Show Context)
Citation Context ...ctions to allow the accumulations to be computed in logarithmic time on an n -processor Erew Pram, even if the tree has greater than logarithmic depth. Straightforward application of Brent's Theorem (=-=Brent, 1974-=-) reduces the processor usage to n= log n , which gives optimal algorithms. The remainder of this paper is organized as follows. In Section 2 we give the definitions of tree reductions and of upwards ... |

185 |
The design and analysis of parallel algorithms
- Akl
- 1989
(Show Context)
Citation Context ...93); the prefix sums problem in turn has applications in the evaluation of polynomials, compiler design, and numerous graph problems including minimum spanning tree and strongly connected components (=-=Akl, 1989-=-). Upwards accumulation can be used to solve some optimization problems on trees, such as minimum covering set and maximal independent set (He, 1986). Other algorithms such as Reingold and Tilford's a... |

122 |
Parallel tree contraction and its application
- Miller, Reif
- 1985
(Show Context)
Citation Context ...e tree in Figure 1. Again, the result is a homogeneous tree. 3 Parallel Tree Contraction Our algorithms for computing accumulations on trees are modifications of parallel tree contraction algorithms (=-=Miller and Reif, 1985-=-; Abrahamson et al., 1989), which reduce a tree to a single value. We present here a description of parallel tree Efficient parallel algorithms for tree accumulations 5 contraction which we generalize... |

86 |
A simple parallel tree contraction algorithm
- ABRAHAMSON, DADOUN, et al.
- 1989
(Show Context)
Citation Context ...in, the result is a homogeneous tree. 3 Parallel Tree Contraction Our algorithms for computing accumulations on trees are modifications of parallel tree contraction algorithms (Miller and Reif, 1985; =-=Abrahamson et al., 1989-=-), which reduce a tree to a single value. We present here a description of parallel tree Efficient parallel algorithms for tree accumulations 5 contraction which we generalize later to the algorithms ... |

61 |
Approximate and exact parallel scheduling with applications to list, tree, and graph problems
- Cole, Vishkin
- 1986
(Show Context)
Citation Context ...tual interference. Their scheme is as follows: (i) Assume all leaves are numbered from left to right, starting with zero. This numbering is easily computed in O(log n) time on O(n= log n) processors (=-=Cole and Vishkin, 1986-=-). (ii) Mark all even-numbered leaves. (iii) For every junction u such that u.l is a marked leaf, perform contractl(u) . (iv) For every junction u not involved in the previous step such that u.r is a ... |

28 |
Upwards and downwards accumulations on trees
- Gibbons
- 1993
(Show Context)
Citation Context ...the prefix sums of a list in logarithmic time on linearly many processors involves building a tree with the list elements as leaves, then performing an upwards and downwards accumulation on the tree (=-=Gibbons, 1993-=-); the prefix sums problem in turn has applications in the evaluation of polynomials, compiler design, and numerous graph problems including minimum spanning tree and strongly connected components (Ak... |

24 |
Algebras for Tree Algorithms. D
- Gibbons
- 1991
(Show Context)
Citation Context ...). Other algorithms such as Reingold and Tilford's algorithm (Reingold and Tilford, 1981) for drawing trees and a two-pass algorithm for completely labelling a tree according to an attribute grammar (=-=Gibbons, 1991-=-) also consist of an upwards followed by a downwards accumulation. For a tree with n elements, these accumulations can be computed naively on a sequential machine in time proportional to n , and on a ... |

9 | Computing downwards accumulations on trees quickly
- Gibbons
- 1996
(Show Context)
Citation Context ...the prefix sums of a list in logarithmic time on linearly many processors involves building a tree with the list elements as leaves, then performing an upwards and downwards accumulation on the tree (=-=Gibbons, 1993-=-); the prefix sums problem in turn has applications in the evaluation of polynomials, compiler design, and numerous graph problems including minimum spanning tree and strongly connected components (Ak... |

8 |
Efficient parallel algorithms for solving some tree problems
- He
- 1986
(Show Context)
Citation Context ...m spanning tree and strongly connected components (Akl, 1989). Upwards accumulation can be used to solve some optimization problems on trees, such as minimum covering set and maximal independent set (=-=He, 1986-=-). Other algorithms such as Reingold and Tilford's algorithm (Reingold and Tilford, 1981) for drawing trees and a two-pass algorithm for completely labelling a tree according to an attribute grammar (... |