Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this formulation is applicable in these domains. We study the complexity of the general problem, and a variant of it where preprocessing is allowed. We show that when the parametric weights are linear functions, algorithms remain tractable even under our relaxed assumptions. Furthermore, we show that if the weights are allowed to be non-linear, the problem becomes NP-hard. We also study the mutli-dimensional version of the problem where the weight functions are parameterized by multiple parameters. We show that even with two parameters, the problem is NP-hard.

翻译：参数路径问题在不同领域独立出现,从运输到金融,在不同的假设下研究这些问题。我们用宽松的假设提出一般路径问题,并描述这些假设如何适用于这些领域。我们研究一般问题的复杂性,以及允许预处理的变式。我们显示,当参数重量是线性功能时,即使在我们放松的假设下,算法仍然可以伸缩。此外,我们显示,如果允许加权非线性,问题就会变成NP硬的。我们还研究加权函数由多个参数参数参数参数参数参数参数参数参数参数参数参数测定的问题的肌肉维度版本。我们显示,即使有两个参数参数参数,问题也是NP硬的。