TY - GEN

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

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

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

M3 - Conference contribution

AN - SCOPUS:85069725088

SN - 9783030250041

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

SP - 365

EP - 377

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

A2 - Colbourn, Charles J.

A2 - Grossi, Roberto

A2 - Pisanti, Nadia

PB - Springer Verlag

T2 - 30th International Workshop on Combinatorial Algorithms, IWOCA 2019

Y2 - 22 July 2019 through 24 July 2019

ER -