## Decentralization and mechanism design for online machine scheduling (2006)

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Venue: | ALGORITHM THEORY - SWAT 2006, VOLUME 4059 OF LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 10 - 1 self |

### BibTeX

@INPROCEEDINGS{Heydenreich06decentralizationand,

author = {Birgit Heydenreich and Rudolf Müller and Marc Uetz},

title = {Decentralization and mechanism design for online machine scheduling },

booktitle = {ALGORITHM THEORY - SWAT 2006, VOLUME 4059 OF LECTURE NOTES IN COMPUTER SCIENCE},

year = {2006},

pages = {136--147},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

We study the online version of the classical parallel machine scheduling problem to minimize the total weighted completion time from a new perspective: We assume that the data of each job, namely its release date rj, its processing time pj and its weight wj is only known to the job itself, but not to the system. Furthermore, we assume a decentralized setting where jobs choose the machine on which they want to be processed themselves. We study this problem from the perspective of algorithmic mechanism design. We introduce the concept of a myopic best response equilibrium, a concept weaker than the dominant strategy equilibrium, but appropriate for online problems. We present a polynomial time, online scheduling mechanism that, assuming rational behavior of jobs, results in an equilibrium schedule that is 3.281-competitive. The mechanism deploys an online payment scheme that induces rational jobs to truthfully report their private data. We also show that the underlying local scheduling policy cannot be extended to a mechanism where truthful reports constitute a dominant strategy equilibrium.

### Citations

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Citation Context ...lized, strategic setting. Related Work and Contribution. Mechanism design in combination with the design of approximation algorithms for scheduling problems has been studied, e.g., by Nisan and Ronen =-=[10]-=-, Archer and Tardos [11], and Kovacs [12]. In those papers, not the jobs but the machines are the selfishly behaving parts of the system, and their private information is the time they need to process... |

185 | Truthful mechanisms for one-parameter agents
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Citation Context .... Related Work and Contribution. Mechanism design in combination with the design of approximation algorithms for scheduling problems has been studied, e.g., by Nisan and Ronen [10], Archer and Tardos =-=[11]-=-, and Kovacs [12]. In those papers, not the jobs but the machines are the selfishly behaving parts of the system, and their private information is the time they need to process the jobs. A scheduling ... |

169 |
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Citation Context ...well-understood in the non-strategic setting with centralized coordination. First, scheduling to minimize the weighted sum of completion times with release dates is NP-hard, even in the off-line case =-=[2]-=-. Second, no online algorithm for the single machine problem can be better than 2-competitive [3] regardless of the question whether or not P=NP, and lower bounds exist for parallel machines, too [4].... |

109 | Towards a characterization of truthful combinatorial auctions - Lavi, Mu’alem, et al. - 2003 |

48 |
Weak monotonicity characterizes deterministic dominant-strategy implementation
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- 2006
(Show Context)
Citation Context ...hful mechanism. Furthermore, we can show that a necessary condition for truthfulness, called weak monotonicity, is not satisfied by the LocalGreedy algorithm. Weak monotonicity has been introduced in =-=[15]-=-. i=1 wk.s7 Discussion It would be interesting to find a constant competitive decentralized online scheduling mechanism such that there is a dominant strategy equilibrium in which the jobs report all ... |

34 | Various optimizers for single stage production - Smith - 1956 |

32 | Mechanism design for online real-time scheduling
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Citation Context ...ehaving parts of the system, and their private information is the time they need to process the jobs. A scheduling model where the jobs are the selfish agents of the system has been studied by Porter =-=[13]-=-. He addresses a single machine scheduling problem, where the private data of each job consists of a release date, its processing time, its weight, and a deadline. In all mentioned papers, the only ac... |

28 |
Fast monotone 3-approximation algorithm for scheduling related machines
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Citation Context ...d Contribution. Mechanism design in combination with the design of approximation algorithms for scheduling problems has been studied, e.g., by Nisan and Ronen [10], Archer and Tardos [11], and Kovacs =-=[12]-=-. In those papers, not the jobs but the machines are the selfishly behaving parts of the system, and their private information is the time they need to process the jobs. A scheduling model where the j... |

22 |
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Citation Context ... [2]. Second, no online algorithm for the single machine problem can be better than 2-competitive [3] regardless of the question whether or not P=NP, and lower bounds exist for parallel machines, too =-=[4]-=-. The best possible algorithm for the single machine case is 2-competitive [5]. For the parallel machine setting, the currently best known online algorithm is 2.61-competitive [6]. In the strategic se... |

16 |
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Citation Context ... than 2-competitive [3] regardless of the question whether or not P=NP, and lower bounds exist for parallel machines, too [4]. The best possible algorithm for the single machine case is 2-competitive =-=[5]-=-. For the parallel machine setting, the currently best known online algorithm is 2.61-competitive [6]. In the strategic setting, selfish agents trying to maximize their own benefit can do so by report... |

14 | Online scheduling to minimize average completion time revisited
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(Show Context)
Citation Context ...h a local sequencing policy that is publicly known, and jobs must be induced to select the machines in such a way that � wj Cj is not too large. Known algorithms with the best performance ratio, e.g. =-=[6, 7]-=-, crucially require central coordination to distribute jobs over machines. An approach by Megow et al. [8], developed for an online setting with release dates and stochastic job durations, however, tu... |

11 |
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(Show Context)
Citation Context ...6, LNCS 4059, pp. 136-147, Springer 2Supported by NWO grant 2004/03545/MaGW ‘Local Decisions in Decentralised Planning Environments’. 3The problem is P | rj | P wj Cj in the notation of Graham et al. =-=[1]-=-.sleads to a setting where the jobs themselves must select the machine to be processed on, and any machine sequences the jobs according to a (known) local sequencing policy. The problem P | rj | � wj ... |

11 | LP-based online scheduling: From single to parallel machines
- Correa, Wagner
(Show Context)
Citation Context ...rallel machines, too [4]. The best possible algorithm for the single machine case is 2-competitive [5]. For the parallel machine setting, the currently best known online algorithm is 2.61-competitive =-=[6]-=-. In the strategic setting, selfish agents trying to maximize their own benefit can do so by reporting strategically about their private information, thus manipulating the resulting schedule. In the m... |

9 | Models and algorithms for stochastic online scheduling
- Megow, Uetz, et al.
(Show Context)
Citation Context ... way that � wj Cj is not too large. Known algorithms with the best performance ratio, e.g. [6, 7], crucially require central coordination to distribute jobs over machines. An approach by Megow et al. =-=[8]-=-, developed for an online setting with release dates and stochastic job durations, however, turns out to be appropriate for being adopted to the decentralized, strategic setting. Related Work and Cont... |

6 | Bounds for the optimal scheduling of n jobs on m processors, Manag. Sci - Eastman, Even, et al. |

2 |
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(Show Context)
Citation Context ...minimize the weighted sum of completion times with release dates is NP-hard, even in the off-line case [2]. Second, no online algorithm for the single machine problem can be better than 2-competitive =-=[3]-=- regardless of the question whether or not P=NP, and lower bounds exist for parallel machines, too [4]. The best possible algorithm for the single machine case is 2-competitive [5]. For the parallel m... |