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A data structure for efficiently managing a set of energy functions
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2021-06-05 , DOI: 10.1007/s10878-021-00758-6
Jacques Carlier , Antoine Jouglet , Eric Pinson , Abderrahim Sahli

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.



中文翻译:

一种有效管理一组能量函数的数据结构

我们考虑对象的集合。每个对象在时间范围开始时都有一个初始能量,以及能量开始随时间减少的过渡时间。在本文中我们描述了冷却箱,用于识别具有最高能量的物体在任何时候一个新的数据结构,具有的值随时间增加。考虑线性函数递减的情况。提出了两个版本,分别用于一组具有相同和不同斜率的函数。有趣的是,我们还确定了使这种方法成为可能的递减函数的基本属性。然后将数据结构推广到非线性递减函数。对于这些版本中的每一个,我们都描述了一个应用程序。

更新日期:2021-06-05
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