A data structure for efficiently managing a set of energy functions

Jacques Carlier (1, 2) , Antoine Jouglet (1, 2) , Eric Pinson (3, 4) , Abderrahim Sahli (5, 6)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 UTC - Université de Technologie de Compiègne
3 UCO - Université Catholique de l'Ouest
4 LARIS - Laboratoire Angevin de Recherche en Ingénierie des Systèmes
5 COSYS-GRETTIA - Génie des Réseaux de Transport Terrestres et Informatique Avancée
6 ESIEE Paris

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.

Domaines: Recherche opérationnelle [math.OC]

Jacques Carlier, Antoine Jouglet, Eric Pinson, Abderrahim Sahli. A data structure for efficiently managing a set of energy functions. Journal of Combinatorial Optimization, 2022, 44 (4), pp.2460-2481. ⟨10.1007/s10878-021-00758-6⟩. ⟨hal-03364775⟩