## An Effective Load Balancing Policy for Geometric Decaying Algorithms

Citations: | 3 - 3 self |

### BibTeX

@MISC{Gil_aneffective,

author = {Joseph Gil and Yossi Matias},

title = {An Effective Load Balancing Policy for Geometric Decaying Algorithms},

year = {}

}

### OpenURL

### Abstract

Parallel algorithms are often first designed as a sequence of rounds, where each round includes any number of independent constant time operations. This so-called work-time presentation is then followed by a processor scheduling implementation ona more concrete computational model. Many parallel algorithms are geometric-decaying in the sense that the sequence of work loads is upper bounded by a decreasing geometric series. A standard scheduling implementation of such algorithms consists of a repeated application of load balancing. We present a more effective, yet as simple, policy for the utilization of load balancing in geometric decaying algorithms. By making a more careful choice of when and how often load balancing should be employed, and by using a simple amortization argument, we showthat the number of required applications of load balancing should be nearly-constant. The policy is not restricted to any particular model of parallel computation, and, up to a constant factor, it is the best possible.

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Citation Context ...cing procedure after each round. Quite a few parallel algorithms are of this type; we note that many logarithmic-time linear work algorithms are geometric-decaying. See, e.g., algorithms described in =-=[14, 13, 18]-=-. The time devoted to the applications of the load balancing algorithms contributes to the total running time of the adapted algorithm, and should therefore be minimized. We show that the standard pol... |

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Citation Context ... n) 3 ) time [11], and in O(lg n) time 1 with high probability [9] (also on the Common crcw [1]). On the Robust crcw pram [2, 12] load balancing can be solved in O(lg lg n) time with high probability =-=[6]-=-. All the above algorithms require linear work. 1 Let lg (i) x j lg(lg (i\Gamma1) x) for i ? 1, and lg (1) x j lg x; lg x j minfi : lg (i) xs2g. The function lg (\Delta) is extremely slow increasing a... |

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Citation Context ...ram in O(lg n= lg lg n) time [4]. Specialized algorithms for load balancing run on the crcw pram in O((lg lg n) 3 ) time [11], and in O(lg n) time 1 with high probability [9] (also on the Common crcw =-=[1]-=-). On the Robust crcw pram [2, 12] load balancing can be solved in O(lg lg n) time with high probability [6]. All the above algorithms require linear work. 1 Let lg (i) x j lg(lg (i\Gamma1) x) for i ?... |

2 |
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Citation Context ...er of tasks is at most 2 \Gammaff(r\Gamma1) (which would be the case if in the first r \Gamma 1 rounds the algorithm was geometric-decaying). Then, the algorithm can be shown to be geometric-decaying =-=[8]. Co-=-nsider a geometric decaying algorithm A whose work is O(n) and running time is �� . Brent's scheduling principle suggests that it may be possible to implement A on a p-processor pram in time O(n=p... |

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