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A data structure for efficiently managing a set of energy functions

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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.

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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.

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Correspondence to Abderrahim Sahli.

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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.

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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

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  • DOI: https://doi.org/10.1007/s10878-021-00758-6

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