An instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP (LinQSPP) decides whether a given QSPP instance is linearizable and determines the corresponding SPP instance in the positive case. We provide a novel linear time algorithm for the LinQSPP on acyclic digraphs which runs considerably faster than the previously best algorithm. The algorithm is based on a new insight revealing that the linearizability of the QSPP for acyclic digraphs can be seen as a local property. Our approach extends to the more general higher-order shortest path problem.

翻译：NP-hard Quadristic 最短路径问题( QSPP) 的例子被称为可线性, 如果它相当于经典最短路径问题( SPP) 的例子, 则称为可线性。 QSPP( LinQSPP) 的线性化问题决定了给定的 QSPP 实例是否可线性, 并在正案中决定相应的 SPP 实例 。 我们为 LinQSPP 提供了一种新颖的线性时间算法, 其运行速度远远快于以往的最佳算法。 算法基于一种新的洞察, 显示QSPP 的可线性可以被视为本地属性 。 我们的方法延伸至更普通的更高级的短路径问题 。</s>