### BibTeX

@MISC{Blelloch_prefixsums,

author = {Guy E. Blelloch},

title = { Prefix Sums and Their Applications},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Experienced algorithm designers rely heavily on a set of building blocks and on the tools needed to put the blocks together into an algorithm. The understanding of these basic blocks and tools is therefore critical to the understanding of algorithms. Many of the blocks and tools needed for parallel

### Citations

272 | Parallel prefix computation
- Ladner, Fischer
- 1980
(Show Context)
Citation Context ...ms suggested by Kogge and Stone [10] and by Stone [19] in the context of recurrence equations. Ladner and Fischer first showed an efficient general-purpose circuit for implementing the scan operation =-=[11]-=-. Brent and Kung, in the context of binary addition, first showed an efficient VLSI layout for a scan circuit [4]. More recent work on implementing scan operations in parallel include the work of Fich... |

260 |
Vector Models for DataParallel Computing
- Blelloch
- 1990
(Show Context)
Citation Context ...scan operations be included in the P-RAM model as primitives and shows how this affects the complexity of various algorithms [1]. The line-of-sight and radix-sort algorithms are discussed by Blelloch =-=[2, 3]-=-. The parallel solution of recurrence problems was first discussed by Karp, Miller and Winograd [9], and parallel algorithms to solve them are given by Kogge and Stone [10], Stone [18, 19] and Chen an... |

166 |
A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
- Kogge, Stone
- 1973
(Show Context)
Citation Context ...on a perfect shuffle network was later suggested by Stone [17] for polynomial evaluation. The optimal algorithm discussed in Section 2 is a slight variation of algorithms suggested by Kogge and Stone =-=[10]-=- and by Stone [19] in the context of recurrence equations. Ladner and Fischer first showed an efficient general-purpose circuit for implementing the scan operation [11]. Brent and Kung, in the context... |

161 |
The organization of computations for uniform recurrence equations
- Karp, Miller, et al.
- 1967
(Show Context)
Citation Context ... of various algorithms [1]. The line-of-sight and radix-sort algorithms are discussed by Blelloch [2, 3]. The parallel solution of recurrence problems was first discussed by Karp, Miller and Winograd =-=[9]-=-, and parallel algorithms to solve them are given by Kogge and Stone [10], Stone [18, 19] and Chen and Kuck [5]. Hyafil and Kung [8] show that the complexity (10) is a lower bound. Schwartz [16] and, ... |

157 | Scans as primitive parallel operations
- Blelloch
- 1989
(Show Context)
Citation Context ...e scan operation on asynchronous machines. Blelloch suggested that certain scan operations be included in the P-RAM model as primitives and shows how this affects the complexity of various algorithms =-=[1]-=-. The line-of-sight and radix-sort algorithms are discussed by Blelloch [2, 3]. The parallel solution of recurrence problems was first discussed by Karp, Miller and Winograd [9], and parallel algorith... |

43 |
An efficient parallel algorithm for the solution of a tridiagonal linear system of equations
- Stone
- 1973
(Show Context)
Citation Context ...d by Blelloch [2, 3]. The parallel solution of recurrence problems was first discussed by Karp, Miller and Winograd [9], and parallel algorithms to solve them are given by Kogge and Stone [10], Stone =-=[18, 19]-=- and Chen and Kuck [5]. Hyafil and Kung [8] show that the complexity (10) is a lower bound. Schwartz [16] and, independently, Mago [14] first suggested the segmented versions of the scans. Blelloch su... |

41 |
Faster optimal parallel prefix sums and list ranking
- Cole, Vishkin
- 1989
(Show Context)
Citation Context ...can operation. A recurrence is a set of equations of the form x i = f i (x i\Gamma1 ; x i\Gamma2 ; \Delta \Delta \Delta ; x i\Gammam ); msi ! n (3) 3 On an CREW P-RAM we can use the scan described in =-=[6]-=- to get a time of O(n=p + lg p= lg lg p). procedure split(A, Flags) I-down / +-prescan(not(Flags)) I-up / n - +-scan(reverse-order(Flags)) in parallel for each index i if (Flags[i]) Index[i] / I-up[i]... |

33 |
Parallel tridiagonal equation solvers
- Stone
- 1975
(Show Context)
Citation Context ...le network was later suggested by Stone [17] for polynomial evaluation. The optimal algorithm discussed in Section 2 is a slight variation of algorithms suggested by Kogge and Stone [10] and by Stone =-=[19]-=- in the context of recurrence equations. Ladner and Fischer first showed an efficient general-purpose circuit for implementing the scan operation [11]. Brent and Kung, in the context of binary additio... |

32 |
On the algorithmic complexity of discrete functions
- Ofman
- 1963
(Show Context)
Citation Context ...ygon. Notes The all-prefix-sums operation has been around for centuries as the recurrence x i = a i +x i\Gamma1 . A parallel circuit to execute the scan operation was first suggested by Ofman in 1963 =-=[15]-=- for the addition of binary numbers. A parallel implementation of scans on a perfect shuffle network was later suggested by Stone [17] for polynomial evaluation. The optimal algorithm discussed in Sec... |

21 | Parallel solutions to geometric problems on the scan model of computation
- Blelloch, Little
- 1988
(Show Context)
Citation Context ...scan operations be included in the P-RAM model as primitives and shows how this affects the complexity of various algorithms [1]. The line-of-sight and radix-sort algorithms are discussed by Blelloch =-=[2, 3]-=-. The parallel solution of recurrence problems was first discussed by Karp, Miller and Winograd [9], and parallel algorithms to solve them are given by Kogge and Stone [10], Stone [18, 19] and Chen an... |

18 |
New bounds for parallel prefix circuits
- Fich
- 1983
(Show Context)
Citation Context ... Brent and Kung, in the context of binary addition, first showed an efficient VLSI layout for a scan circuit [4]. More recent work on implementing scan operations in parallel include the work of Fich =-=[7]-=- and of Lakshmivarahan, Yang and Dhall [12], which give improvements over the circuit of Ladner and Fischer, and of Lubachevsky and Greenberg [13], which demonstrates the implementation of the scan op... |

17 | The chip complexity of binary arithmetic
- Brent, Kung
- 1980
(Show Context)
Citation Context ...first showed an efficient general-purpose circuit for implementing the scan operation [11]. Brent and Kung, in the context of binary addition, first showed an efficient VLSI layout for a scan circuit =-=[4]-=-. More recent work on implementing scan operations in parallel include the work of Fich [7] and of Lakshmivarahan, Yang and Dhall [12], which give improvements over the circuit of Ladner and Fischer, ... |

14 |
Time and parallel processor bounds for linear recurrence systems
- Chen, Kuck
- 1988
(Show Context)
Citation Context ...arallel solution of recurrence problems was first discussed by Karp, Miller and Winograd [9], and parallel algorithms to solve them are given by Kogge and Stone [10], Stone [18, 19] and Chen and Kuck =-=[5]-=-. Hyafil and Kung [8] show that the complexity (10) is a lower bound. Schwartz [16] and, independently, Mago [14] first suggested the segmented versions of the scans. Blelloch suggested many uses of t... |

14 |
The complexity of parallel evaluation of linear recurrence
- Hyafil, Kung
- 1975
(Show Context)
Citation Context ...ecurrence problems was first discussed by Karp, Miller and Winograd [9], and parallel algorithms to solve them are given by Kogge and Stone [10], Stone [18, 19] and Chen and Kuck [5]. Hyafil and Kung =-=[8]-=- show that the complexity (10) is a lower bound. Schwartz [16] and, independently, Mago [14] first suggested the segmented versions of the scans. Blelloch suggested many uses of these scans including ... |

4 |
A Network of Computers to Execute Reduction Languages
- Magó
- 1979
(Show Context)
Citation Context ...ithms to solve them are given by Kogge and Stone [10], Stone [18, 19] and Chen and Kuck [5]. Hyafil and Kung [8] show that the complexity (10) is a lower bound. Schwartz [16] and, independently, Mago =-=[14]-=- first suggested the segmented versions of the scans. Blelloch suggested many uses of these scans including the quicksort algorithm and the line-drawing algorithm presented in Sections 5.1 and 6.1 [2]... |

4 |
Parallel Processsing with the Perfect Shuffle
- Stone
- 1971
(Show Context)
Citation Context ...o execute the scan operation was first suggested by Ofman in 1963 [15] for the addition of binary numbers. A parallel implementation of scans on a perfect shuffle network was later suggested by Stone =-=[17]-=- for polynomial evaluation. The optimal algorithm discussed in Section 2 is a slight variation of algorithms suggested by Kogge and Stone [10] and by Stone [19] in the context of recurrence equations.... |

4 | Efficient Asynchronous Parallel Prefix Algorithms - Lubachevsky, Greenberg, et al. - 1987 |

3 |
Optimal Parallel Prefix Circuits with (size + depth
- Lakshmivarahan, Yang, et al.
- 1987
(Show Context)
Citation Context ...addition, first showed an efficient VLSI layout for a scan circuit [4]. More recent work on implementing scan operations in parallel include the work of Fich [7] and of Lakshmivarahan, Yang and Dhall =-=[12]-=-, which give improvements over the circuit of Ladner and Fischer, and of Lubachevsky and Greenberg [13], which demonstrates the implementation of the scan operation on asynchronous machines. Blelloch ... |

2 |
Efficient Asynchronous Parallel Prefix Algorithms
- Simple
- 1987
(Show Context)
Citation Context ...g scan operations in parallel include the work of Fich [7] and of Lakshmivarahan, Yang and Dhall [12], which give improvements over the circuit of Ladner and Fischer, and of Lubachevsky and Greenberg =-=[13]-=-, which demonstrates the implementation of the scan operation on asynchronous machines. Blelloch suggested that certain scan operations be included in the P-RAM model as primitives and shows how this ... |