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

Fumito Miyake, Eiji Takimoto, Kohei Hatano

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

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.

本文言語英語
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
出版社Springer Verlag
ページ365-377
ページ数13
ISBN(印刷版)9783030250041
DOI
出版ステータス出版済み - 2019
イベント30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, イタリア
継続期間: 7月 23 20197月 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)
11638 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議30th International Workshop on Combinatorial Algorithms, IWOCA 2019
国/地域イタリア
CityPisa
Period7/23/197/25/19

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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