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Horizontally Elastic Edge Finder Rule for Cumulative Constraint Based on Slack and Density

Authors Roger Kameugne , Sévérine Fetgo Betmbe , Thierry Noulamo , Clémentin Tayou Djamegni

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Author Details

Roger Kameugne
  • Faculty of Sciences, Department of Mathematics and Computer Science, University of Maroua, Cameroon
Sévérine Fetgo Betmbe
  • Faculty of Sciences, Department of Mathematics and Computer Science, University of Dschang, Cameroon
Thierry Noulamo
  • UIT Fotso Victor of Bandjoun, Department of Computer Engineering, University of Dschang, Cameroon
Clémentin Tayou Djamegni
  • Faculty of Sciences, Department of Mathematics and Computer Science, University of Dschang, Cameroon
  • UIT Fotso Victor of Bandjoun, Department of Computer Engineering, University of Dschang, Cameroon

Acknowledgements

The authors thank Dr. Dany Nantchouang and Prof. Emmanuel Hebrard for their proofreading.

Cite AsGet BibTex

Roger Kameugne, Sévérine Fetgo Betmbe, Thierry Noulamo, and Clémentin Tayou Djamegni. Horizontally Elastic Edge Finder Rule for Cumulative Constraint Based on Slack and Density. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CP.2023.20

Abstract

In this paper, we propose an enhancement of the filtering power of the edge finding rule, based on the Profile and the TimeTable data structures. The minimal slack and the maximum density criteria are used to select potential task intervals for the edge finding rule. The strong detection rule of the horizontally elastic edge finder of Fetgo and Tayou is then applied on those intervals, which results in a new filtering rule, named Slack-Density Horizontally Elastic Edge Finder. The new rule subsumes the edge finding rule and it is not comparable to the Gingras and Quimper horizontally elastic edge finder rule and the TimeTable edge finder rule. A two-phase filtering algorithm of complexity 𝒪(n²) (where n is the number of tasks sharing the resource) is proposed for the new rule. Improvements based on the TimeTable are obtained by considering fix part of external tasks which overlap with the potential task intervals. The detection and the adjustment of the improve algorithm are further increased, while the algorithm remains quadratic. Experimental results, on a well-known suite of benchmark instances of Resource-Constrained Project Scheduling Problems, show that the propounded algorithms are competitive with the state-of-the-art algorithms, in terms of running time and tree search reduction.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Planning and scheduling
  • Theory of computation → Constraint and logic programming
Keywords
  • Horizontally Elastic Scheduling
  • Edge Finder Rule
  • Profile
  • TimeTable
  • Resource-Constrained Project Scheduling Problem

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