### 抄録

We consider a single machine scheduling problem to minimize total flow time under precedence constraints, which is NP-hard. Matsumoto et al. proposed an exact algorithm that consists of two phases: first construct a Multi-valued Decision Diagram (MDD) to represent feasible permutations of jobs, and then find the shortest path in the MDD which corresponds to the optimal solution. Although their algorithm performs significantly better than standard IP solvers for problems with dense constraints, the performance rapidly diminishes when the number of constraints decreases, which is due to the exponential growth of MDDs. In this paper, we introduce an equivalence relation among feasible permutations and show that it suffices to construct an MDD that maintains only one representative for each equivalence class. Experimental results show that our algorithm outperforms Matsumoto et al.’s algorithm for problems with sparse constraints, while keeping good performance for dense constraints. Moreover, we show that Matsumoto et al.’s algorithm can be extended for solving a more general problem of minimizing weighted total flow time.

元の言語 | 英語 |
---|---|

ホスト出版物のタイトル | Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings |

編集者 | Charles J. Colbourn, Roberto Grossi, Nadia Pisanti |

出版者 | Springer Verlag |

ページ | 365-377 |

ページ数 | 13 |

ISBN（印刷物） | 9783030250041 |

DOI | |

出版物ステータス | 出版済み - 1 1 2019 |

イベント | 30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, イタリア 継続期間: 7 23 2019 → 7 25 2019 |

### 出版物シリーズ

名前 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

巻 | 11638 LNCS |

ISSN（印刷物） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### 会議

会議 | 30th International Workshop on Combinatorial Algorithms, IWOCA 2019 |
---|---|

国 | イタリア |

市 | Pisa |

期間 | 7/23/19 → 7/25/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### これを引用

*Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings*(pp. 365-377). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 11638 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-25005-8_30

**Succinct representation of linear extensions via MDDs and its application to scheduling under precedence constraints.** / Miyake, Fumito; Takimoto, Eiji; hatano, kohei.

研究成果: 著書/レポートタイプへの貢献 › 会議での発言

*Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 11638 LNCS, Springer Verlag, pp. 365-377, 30th International Workshop on Combinatorial Algorithms, IWOCA 2019, Pisa, イタリア, 7/23/19. https://doi.org/10.1007/978-3-030-25005-8_30

}

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T1 - Succinct representation of linear extensions via MDDs and its application to scheduling under precedence constraints

AU - Miyake, Fumito

AU - Takimoto, Eiji

AU - hatano, kohei

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider a single machine scheduling problem to minimize total flow time under precedence constraints, which is NP-hard. Matsumoto et al. proposed an exact algorithm that consists of two phases: first construct a Multi-valued Decision Diagram (MDD) to represent feasible permutations of jobs, and then find the shortest path in the MDD which corresponds to the optimal solution. Although their algorithm performs significantly better than standard IP solvers for problems with dense constraints, the performance rapidly diminishes when the number of constraints decreases, which is due to the exponential growth of MDDs. In this paper, we introduce an equivalence relation among feasible permutations and show that it suffices to construct an MDD that maintains only one representative for each equivalence class. Experimental results show that our algorithm outperforms Matsumoto et al.’s algorithm for problems with sparse constraints, while keeping good performance for dense constraints. Moreover, we show that Matsumoto et al.’s algorithm can be extended for solving a more general problem of minimizing weighted total flow time.

AB - We consider a single machine scheduling problem to minimize total flow time under precedence constraints, which is NP-hard. Matsumoto et al. proposed an exact algorithm that consists of two phases: first construct a Multi-valued Decision Diagram (MDD) to represent feasible permutations of jobs, and then find the shortest path in the MDD which corresponds to the optimal solution. Although their algorithm performs significantly better than standard IP solvers for problems with dense constraints, the performance rapidly diminishes when the number of constraints decreases, which is due to the exponential growth of MDDs. In this paper, we introduce an equivalence relation among feasible permutations and show that it suffices to construct an MDD that maintains only one representative for each equivalence class. Experimental results show that our algorithm outperforms Matsumoto et al.’s algorithm for problems with sparse constraints, while keeping good performance for dense constraints. Moreover, we show that Matsumoto et al.’s algorithm can be extended for solving a more general problem of minimizing weighted total flow time.

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U2 - 10.1007/978-3-030-25005-8_30

DO - 10.1007/978-3-030-25005-8_30

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings

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A2 - Grossi, Roberto

A2 - Pisanti, Nadia

PB - Springer Verlag

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