## Proportionate progress: A notion of fairness in resource allocation (1996)

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Venue: | Algorithmica |

Citations: | 260 - 25 self |

### BibTeX

@ARTICLE{Baruah96proportionateprogress:,

author = {S. K. Baruah and N. K. Cohen and C. G. Plaxton and D. A. Varvel},

title = {Proportionate progress: A notion of fairness in resource allocation},

journal = {Algorithmica},

year = {1996},

volume = {15},

pages = {600--625}

}

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### Abstract

Given a set of n tasks and m resources, where each task x has a rational weight x:w = x:e=x:p; 0 < x:w < 1, a periodic schedule is one that allocates a resource to a task x for exactly x:e time units in each interval [x:p k; x:p (k + 1)) for all k 2 N. We de ne a notion of proportionate progress, called P-fairness, and use it to design an e cient algorithm which solves the periodic scheduling problem. Keywords: Euclid's algorithm, fairness, network ow, periodic scheduling, resource allocation.

### Citations

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(Show Context)
Citation Context ...n instance is feasible), and (ii) the "scheduling" problem (i.e., actually constructing the schedule for a given feasible instance). Many sets of constraints result in an intractable decisio=-=n problem [5]-=-. The periodic scheduling problem was first discussed by Liu in 1969 [11]. Given a set of n tasks and m resources, where each task x has rational weight x:w = x:e=x:p, 0 ! x:w ! 1, a periodic schedule... |

3067 | Scheduling Algorithms for Multiprogramming in a Hard Real Time Environment,ā€¯Journal of the Association for Computing Machinery
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Citation Context ...d to single-resource scheduling. There are several optimal single-resource scheduling algorithms for the periodic scheduling problem. The Earliest Deadline algorithm of Liu and Layland is one example =-=[12]. Non-=-e of them extends directly to multiple resources. As Liu pointed out, "the simple fact that a task can use only one [resource] even when several [resources] are free at the same time adds a surpr... |

800 |
Flows in networks
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Citation Context ...Gamma1 x=0 x:wsm can be scheduled by the resource sharing algorithm mentioned above. Baruah, Howell, and Rosier [1] used this fact, the network reduction of Horn [7], and the Ford-Fulkerson algorithm =-=[4]-=- to show that there are solutions to the periodic scheduling problem. Thus, the decision problem for such a periodic task system reduces to checking that P n\Gamma1 x=0 x:wsm. A method similar to that... |

385 | Expected Time Bounds for Selection
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Citation Context ...ll to subroutine Compare can be used to determine the relative priority of any two contending tasks. Thus, by applying subroutine Compare within any optimal comparisonbased selection algorithm (e.g., =-=[2]-=-), we can obtain an implementation of Algorithm PF that makes O(n) calls to subroutine Compare to decide which m-subset of the n tasks to schedule in any given slot. This simple approach yields a poly... |

241 | Integer programming with a fixed number of variables
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Citation Context ... been proposed for 2-ILP, that is, integer linear programming with two variables [6, 8, 13, 14]. (ILP is NP-complete in general, but can be solved in polynomial-time for any fixed number of variables =-=[9]-=-.) Deng has extensively studied the relationship between GCD and 2-ILP [3]. Our P-fair scheduling algorithm produces schedules with a large number of preemptions. It would be interesting to investigat... |

194 | Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor
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Citation Context ...ma1 x=0 x:w ? m cannot be scheduled. If resource sharing is allowed, those in which P n\Gamma1 x=0 x:wsm can be scheduled by the resource sharing algorithm mentioned above. Baruah, Howell, and Rosier =-=[1]-=- used this fact, the network reduction of Horn [7], and the Ford-Fulkerson algorithm [4] to show that there are solutions to the periodic scheduling problem. Thus, the decision problem for such a peri... |

77 |
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Citation Context ...haring is allowed, those in which P n\Gamma1 x=0 x:wsm can be scheduled by the resource sharing algorithm mentioned above. Baruah, Howell, and Rosier [1] used this fact, the network reduction of Horn =-=[7]-=-, and the Ford-Fulkerson algorithm [4] to show that there are solutions to the periodic scheduling problem. Thus, the decision problem for such a periodic task system reduces to checking that P n\Gamm... |

49 |
Scheduling algorithms for multiprocessors in a hard real-time environment
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(Show Context)
Citation Context ...ly constructing the schedule for a given feasible instance). Many sets of constraints result in an intractable decision problem [5]. The periodic scheduling problem was first discussed by Liu in 1969 =-=[11]-=-. Given a set of n tasks and m resources, where each task x has rational weight x:w = x:e=x:p, 0 ! x:w ! 1, a periodic schedule is one that allocates a resource to a task x for exactly x:e time units ... |

38 |
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Citation Context ...n the time interval [x:s + x:p \Delta k; x:s + x:p \Delta k + x:d) for all k 2 N. Leung's application of the Least Slack algorithm to this problem represents a recent improvement on Earliest Deadline =-=[10]-=-, for the case where scheduling decisions are not required to occur at integer time instants. Leung was able to show that Least Slack schedules all instances that can be scheduled by Earliest Deadline... |

15 |
A Polynomial Algorithm for the Two-variable Integer Programming Problem
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Citation Context ...mpare subroutine appears to be closely related to Euclid's GCD algorithm, as 23 well as to various algorithms that have been proposed for 2-ILP, that is, integer linear programming with two variables =-=[6, 8, 13, 14]-=-. (ILP is NP-complete in general, but can be solved in polynomial-time for any fixed number of variables [9].) Deng has extensively studied the relationship between GCD and 2-ILP [3]. Our P-fair sched... |

11 |
A Polynomial-time Algorithm for the Knapsack Problem with Two Variables
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Citation Context ...mpare subroutine appears to be closely related to Euclid's GCD algorithm, as 23 well as to various algorithms that have been proposed for 2-ILP, that is, integer linear programming with two variables =-=[6, 8, 13, 14]-=-. (ILP is NP-complete in general, but can be solved in polynomial-time for any fixed number of variables [9].) Deng has extensively studied the relationship between GCD and 2-ILP [3]. Our P-fair sched... |

10 |
Production Sets with Indivisibilities, Part II: The Case of Two Activities
- Scarf
- 1981
(Show Context)
Citation Context ...mpare subroutine appears to be closely related to Euclid's GCD algorithm, as 23 well as to various algorithms that have been proposed for 2-ILP, that is, integer linear programming with two variables =-=[6, 8, 13, 14]-=-. (ILP is NP-complete in general, but can be solved in polynomial-time for any fixed number of variables [9].) Deng has extensively studied the relationship between GCD and 2-ILP [3]. Our P-fair sched... |

7 |
Production sets with indivisibilities. Part I: generalities
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- 1981
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Citation Context |

3 |
Mathematical Programming: Complexity and Applications
- Deng
- 1989
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Citation Context ...iables [6, 8, 13, 14]. (ILP is NP-complete in general, but can be solved in polynomial-time for any fixed number of variables [9].) Deng has extensively studied the relationship between GCD and 2-ILP =-=[3]-=-. Our P-fair scheduling algorithm produces schedules with a large number of preemptions. It would be interesting to investigate algorithms for solving the periodic scheduling problem which minimize th... |