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A survey on how the structure of precedence constraints may change the complexity class of scheduling problems

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Abstract

This survey aims to demonstrate that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed, many problems can be \(\mathcal {NP}\)-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. Additionally, the existence of many very exciting challenges in this research area is underlined.

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Authors and Affiliations

  1. Ecole des Mines de Nantes, 4 rue Alfred Kastler, B.P. 20722, 44307, Nantes Cedex 3, France

    D. Prot & O. Bellenguez-Morineau

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  1. D. Prot
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  2. O. Bellenguez-Morineau
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Correspondence to D. Prot.

Appendix: List of results

Appendix: List of results

For an easier reading of all the complexity results that are reviewed in this survey, we proposed a synthesis in the following tables. In each table, we write the polynomial cases, some open cases (the ones that seem the most promising in our opinion) and the \(\mathcal {NP}\)-hard problems.

See Tables 1, 2 and 3.

Table 1 Complexity results for single-machine problems
Full size table
Table 2 Complexity results for parallel machine problems without preemption
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Table 3 Complexity results for parallel machine problems with preemption
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Prot, D., Bellenguez-Morineau, O. A survey on how the structure of precedence constraints may change the complexity class of scheduling problems. J Sched 21, 3–16 (2018). https://doi.org/10.1007/s10951-017-0519-z

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