Abstract
We consider a collection of objects. Each object has an initial energy at the start of the time horizon, and a transition time at which the energy begins to decrease over time. In this paper we describe the Cooling Box, a new data structure for identifying the object with the highest energy at any time t, with values of t increasing over time. The case of decreasing linear functions is considered. Two versions are proposed, for a set of functions with identical and non-identical slopes respectively. Interestingly, we also identify the basic property of decreasing functions that makes this method possible. The data structure is then generalized to decreasing functions that are not linear. For each of these versions we describe an application.
Similar content being viewed by others
References
Adelson-Velskii G, Landis E (1962) An algorithm for the organization of information. Sov Math Dokl 3:1259263
Baptiste P, Le Pape C, Nuijten W (2001) Constraint-based scheduling, applying constraint programming to scheduling problems, international series in operations research and management science. Kluwer, Philadelphia
Carlier J (1984) Problèmes d’ordonnancement à contraintes de ressources : algorithmes et complexité. Ph.D. thesis, Université Pierre et Marie Curie (Paris VI). Doctorat d’état es Sciences
Carlier J, Pinson E, Sahli A, Jouglet A (2020) An \(o(n^2)\) algorithm for time-bound adjustments for the cumulative scheduling problem. Eur J Oper Res 286:468–476
Erschler J, Lopez P (1990) Energy-based approach for task scheduling under time and resources constraints. In: Proceedings of the \(2^{\rm nd}\) international workshop on project management and scheduling, pp 115–121
Jouglet A, Carlier J (2011) Dominance rules in combinatorial optimization problems. Eur J Oper Res 212:433–444. https://doi.org/10.1016/j.ejor.2010.11.008
Acknowledgements
The authors would like to thank the anonymous reviewers of this article regarding their propositions to improve this article.
Funding
These works are partially financed by the Project 2018-0062H of the Gaspard Monge Program for Optimization, operations research, and their interactions with data science.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
Authors have received the conference best paper award at IESM’2019 on a preliminary version of this paper. The authors declare that they have no other conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Carlier, J., Jouglet, A., Pinson, E. et al. A data structure for efficiently managing a set of energy functions. J Comb Optim 44, 2460–2481 (2022). https://doi.org/10.1007/s10878-021-00758-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-021-00758-6