关于时间依赖图的路排序
On path ranking in time-dependent graphs
摘要：
在本文中，我们研究了时间依赖图的一个性质，称为路径排名不变性。广义地说，时间依赖图是路径排名不变的，如果它的路径的顺序（w.r.t.行程时间）与开始时间无关。在本文中，我们表明，如果一个图是路径排名不变的，一个大类的时间相关的车辆路径问题的解决方案，可以通过解决适当定义的（和更简单的）时间无关的路径问题。我们还展示了如何通过求解线性规划来检查此属性。如果检查失败，则线性规划的解可用于确定紧下限。为了评估这些见解的价值，下限已被嵌入到枚举计划。对时间依赖版本的\textit{Travelling Salesman Problem}和\textit{Rural Postman Problem}的计算结果表明，新的研究结果允许超越国家的最先进的算法。
英文摘要：
In this paper we study a property of time-dependent graphs, dubbed path ranking invariance. Broadly speaking, a time-dependent graph is path ranking invariant if the ordering of its paths (w.r.t. travel time) is independent of the start time. In this paper we show that, if a graph is path ranking invariant, the solution of a large class of time-dependent vehicle routing problems can be obtained by solving suitably defined (and simpler) time-independent routing problems. We also show how this property can be checked by solving a linear program. If the check fails, the solution of the linear program can be used to determine a tight lower bound. In order to assess the value of these insights, the lower bounds have been embedded into an enumerative scheme. Computational results on the time-dependent versions of the \textit{Travelling Salesman Problem} and the \textit{Rural Postman Problem} show that the new findings allow to outperform state-of-the-art algorithms.
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