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

Fumito Miyake, Eiji Takimoto, kohei hatano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings
EditorsCharles J. Colbourn, Roberto Grossi, Nadia Pisanti
PublisherSpringer Verlag
Pages365-377
Number of pages13
ISBN (Print)9783030250041
DOIs
Publication statusPublished - Jan 1 2019
Event30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, Italy
Duration: Jul 23 2019Jul 25 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11638 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference30th International Workshop on Combinatorial Algorithms, IWOCA 2019
CountryItaly
CityPisa
Period7/23/197/25/19

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Miyake, F., Takimoto, E., & hatano, K. (2019). Succinct representation of linear extensions via MDDs and its application to scheduling under precedence constraints. In C. J. Colbourn, R. Grossi, & N. Pisanti (Eds.), 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); Vol. 11638 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-25005-8_30