## A Survey of Cost Models for Algorithmic Skeletons (1999)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Hamdan99asurvey,

author = {Mohammad M. Hamdan},

title = {A Survey of Cost Models for Algorithmic Skeletons},

institution = {},

year = {1999}

}

### OpenURL

### Abstract

This report presents a survey of performance models for parallel algorithmic skeletons. First, higher-order functions (HOFs) are presented according to the modelled skeletons. Next, the corresponding parallel implementations (skeletons) for the HOFs are discussed with the performance models that were constructed for the skeletons. 1 Introduction Effective portability depends crucially on the predictability of performance. Therefore, accurate performance models are required to predict the behaviour of a given skeleton before successfully porting the application that is currently using this skeleton. For the importance of performance models for algorithmic skeletons, this report aims to survey some of them. 2 Higher Order Functions for the Modeled Skeletons This section presents briefly the HOFs used to describe the skeletons in Section 3. The HOFs are classified into two major classes: general and application specific HOFs. 2.1 General Higher Order Functions The HOFs are presented i...

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(Show Context)
Citation Context ...l t x: tests if a problem x is trivial. ffl s x: solves a problem x. ffl d x: divides a larger task x into sub-tasks. ffl c ((map DC ...) x): combines the sub-results to produce the main result. Cole =-=[5]-=- has also presented a HOF for his fixed degree divide and conquer (FDDC) skeleton. This is a special form of the general divide and conquer skeleton where the number of sub-problems to be divided are ... |

69 |
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(Show Context)
Citation Context ...nded to cover scalability analysis using the isoefficiency function [6]. 4 Cost Models for Skeleton-Oriented Programming The following researchers: S. Pelagatti [15], R. Rangaswami[17], D. Skillicorn =-=[18]-=- and H. W. To [21] have developed cost modelling systems in conjunction with their models for skeleton-oriented programming. Before outlining the cost models they have developed for their skeletons, w... |

58 | A Cost Calculus for Parallel Functional Programming
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(Show Context)
Citation Context ...or the 2-D torus topology. Also, cost models were developed for the tree topology. All Topologies Table 4 outlines the skeletons which have one cost model for the four topologies. D. Skillicorn et al =-=[18, 19]-=- have developed a cost calculus for the BirdMeertens Formalism (BMF) [1]. First we briefly describe BMF before describing skeleton cost model s fold C m ideal s fold = C f ( n p + 1 + log p 1 2 + log ... |

43 |
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Citation Context ...le. ffl solve prob: solves an indivisible instance of a problem prob. ffl divide prob: divides the problem prob into sub-problems. ffl combine prob sols: combines the solutions sols. Darlington et al =-=[9]-=- have presented a HOF for the divide and conquer (DC) skeleton. Similar to the recursively partitioned skeleton, the idea is to split larger tasks into sub-tasks and combine the results obtained by so... |

42 |
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Citation Context ...logy. All Topologies Table 4 outlines the skeletons which have one cost model for the four topologies. D. Skillicorn et al [18, 19] have developed a cost calculus for the BirdMeertens Formalism (BMF) =-=[1]-=-. First we briefly describe BMF before describing skeleton cost model s fold C m ideal s fold = C f ( n p + 1 + log p 1 2 + log p 2 2 + T 1 com ( p 1 +p 2 2 ) g fold C f ( n p + 1 + log p 1 2 + log p ... |

38 |
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Citation Context ...ty function. Also, the models were extended to cover scalability analysis using the isoefficiency function [6]. 4 Cost Models for Skeleton-Oriented Programming The following researchers: S. Pelagatti =-=[15]-=-, R. Rangaswami[17], D. Skillicorn [18] and H. W. To [21] have developed cost modelling systems in conjunction with their models for skeleton-oriented programming. Before outlining the cost models the... |

28 |
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Citation Context ...el was validated on a 74 node T800 Transputer based multicomputer system. The difference between the measured speedup and the predicted speedup by the model was claimed it did not exceed 5%. Bratvold =-=[2]-=- has also developed a performance model for the FARM skeleton. The completion time for the skeleton was given as follows: TC = T start + T run + T close where T start + T close = PwsFarm startclose ad... |

19 | Optimising the Parallel Behaviour of Combinations of Program Components
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(Show Context)
Citation Context ...ability analysis using the isoefficiency function [6]. 4 Cost Models for Skeleton-Oriented Programming The following researchers: S. Pelagatti [15], R. Rangaswami[17], D. Skillicorn [18] and H. W. To =-=[21]-=- have developed cost modelling systems in conjunction with their models for skeleton-oriented programming. Before outlining the cost models they have developed for their skeletons, we need first to pr... |

17 | A cost analysis for a higher-order parallel programming model
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Citation Context ...the models were extended to cover scalability analysis using the isoefficiency function [6]. 4 Cost Models for Skeleton-Oriented Programming The following researchers: S. Pelagatti [15], R. Rangaswami=-=[17]-=-, D. Skillicorn [18] and H. W. To [21] have developed cost modelling systems in conjunction with their models for skeleton-oriented programming. Before outlining the cost models they have developed fo... |

13 |
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Citation Context ...However, it may be possible to modify the model and make it more general then instantiate it with machine parameters for other architecture similar to Darlington et al's performance models. Busvine's =-=[3]-=- performance model for the FARM skeleton is as follows: T Farm = max(Ns(T Rec +K Rec + T Comms ) + TBase ; (N=W )s(T Task +KW orker +K T reesT Comms )) +Ns(T Combine +K Combine ) +K W Setup where T Re... |

12 |
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Citation Context ...ersion of DC is similar to Cole's FDDC skeleton except that internal processors of the tree topology also perform work. The performance model for the DC skeleton which was developed by Sreekantaswamy =-=[20]-=- for speedup with startup cost taken into account is as follows: SP (N) = MT e T startup + M \Gamma1 SN where steady state throughput is S i = S i\Gamma1 / T e (i) + fi e \Gamma T s (i) \Gamma T j (i)... |

10 | CLUMPS: a candidate model of efficient, general purpose parallel computation
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(Show Context)
Citation Context ...application specific HOFs. 2.1 General Higher Order Functions The HOFs are presented in this section according to the classification used to present their corresponding skeletons which was taken from =-=[4]-=-. 2.1.1 Recursively Partitioned A recursively partitioned skeleton works by generating subordinate problems as a result of dividing the original problem. These generated problems will also be divided ... |

10 | The performance of parallel algorithmic skeletons
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(Show Context)
Citation Context ...fic parallel programs. Normally, program developers who use such skeletons are experts of the problem field of research. In other words, knowledge is required for using such skeletons. Deldarie et al =-=[13]-=- have presented performance models for special cases of skeletons related to image processing. One skeleton called local window (LW) which transforms an image into another image. Each pixel in the res... |

9 |
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(Show Context)
Citation Context ...binary tree on a grid of processors. Although, Feldcamp et al [8] did not present a HOF for the DC skeleton they developed. Their skeleton was integrated in the program development environment Parsec =-=[12]-=-. The DC was implemented as a binary tree on a Transputer network. This version of DC is similar to Cole's FDDC skeleton except that internal processors of the tree topology also perform work. The per... |

7 | Introduction to Probabilistic Performance Modelling of Parallel Applications
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(Show Context)
Citation Context ... of the cost model against a parallel machine. ffl Has the cost model been combined with other cost models. 6 Related Work There is lots of work on performance modelling of parallel programs. Jonkers =-=[14]-=- has presented a survey of of probabilistic performance modelling techniques and their applicability to parallel applications. He outlined different modelling techniques: queuing, task graph, petri ne... |

6 | Modeling Performance of Parallel Programs
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(Show Context)
Citation Context ...f probabilistic performance modelling techniques and their applicability to parallel applications. He outlined different modelling techniques: queuing, task graph, petri net and hybrid models. Wagner =-=[22]-=- has reviewed current approaches to modelling (both analytical modeling based on system parameters, and structural modeling based on the structure of the program. Also, he proposed a combination of th... |

3 |
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(Show Context)
Citation Context ...eletons in that they are integrated into one system for skeleton-oriented parallel programming. S. Pelagatti [15] has participated in developing an explicit parallel programming language called P 3 L =-=[11, 7]-=-. She has developed cost models for the pipe and process farm skeletons. R. Rangaswami [17] has developed a parallel programming model called HOPP for skeleton-oriented programming. HOPP stands for Hi... |

3 |
et al. Structured Parallel Programming
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(Show Context)
Citation Context ... form of pipeline-like skeletons) consists of a number of stages where parallelism is exploited by operating on a flow of data that passes through the various stages of the pipeline. Darlington et al =-=[10]-=- have presented a HOF for the pipe skeletons, which is: P IPE :: [[ff] ! [ff]] ! [ff] ! [ff] PIPE = foldr1 ( o ) 2.2 Application-based Higher Order Functions There were no HOFs presented for the model... |

3 |
et al. The P L Language: An Introduction
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Citation Context ...eletons in that they are integrated into one system for skeleton-oriented parallel programming. S. Pelagatti [15] has participated in developing an explicit parallel programming language called P 3 L =-=[11, 7]-=-. She has developed cost models for the pipe and process farm skeletons. R. Rangaswami [17] has developed a parallel programming model called HOPP for skeleton-oriented programming. HOPP stands for Hi... |

3 |
Exploiting Prallelism in Functional Languages: a Paradigm -Oriented Approach
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(Show Context)
Citation Context ...original problem. These generated problems will also be divided further in an attempt to solve them. Two well known algorithms that belong to this category are quick-sort and least-cost search. Rabhi =-=[16]-=- gave a HOF describing this skeleton: rp$ ind solve divide combine prob --- ind prob = solve prob --- otherwise = combine prob (map (rp$ ind solve divide combine) (divide prob)) where: ffl ind prob: r... |

2 |
et al. Towards a Skeleton-based Parallel Programming Environment
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(Show Context)
Citation Context ...er researchers in the field to work on performance models for skeletons. 1 The H-tree implementation is a well known layout of a complete binary tree on a grid of processors. Although, Feldcamp et al =-=[8]-=- did not present a HOF for the DC skeleton they developed. Their skeleton was integrated in the program development environment Parsec [12]. The DC was implemented as a binary tree on a Transputer net... |

1 |
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(Show Context)
Citation Context ... execution time for the SAM and LW skeletons was presented as a generic higher order complexity function. Also, the models were extended to cover scalability analysis using the isoefficiency function =-=[6]-=-. 4 Cost Models for Skeleton-Oriented Programming The following researchers: S. Pelagatti [15], R. Rangaswami[17], D. Skillicorn [18] and H. W. To [21] have developed cost modelling systems in conjunc... |