Generalized parametric path problems
Kshitij Gajjar, Girish Varma, Prerona Chatterjee, Jaikumar Radhakrishnan
Abstract
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 multi-dimensional version of the problem where the weight functions are parameterized by multiple parameters. We show that even with two parameters, this problem is NP-hard.
BibTeX
@InProceedings{pmlr-v161-gajjar21a,
title = {Generalized parametric path problems},
author = {Gajjar, Kshitij and Varma, Girish and Chatterjee, Prerona and Radhakrishnan, Jaikumar},
booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence},
pages = {536--546},
year = {2021},
editor = {de Campos, Cassio and Maathuis, Marloes H.},
volume = {161},
series = {Proceedings of Machine Learning Research},
month = {27--30 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v161/gajjar21a/gajjar21a.pdf},
url = {https://proceedings.mlr.press/v161/gajjar21a.html},
abstract = {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 multi-dimensional version of the problem where the weight functions are parameterized by multiple parameters. We show that even with two parameters, this problem is NP-hard.}
}