The $k$path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing
Abstract
In this paper, we investigate the $k$path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `treelike' structure. We exploit this property to design an efficient algorithm for our industrial problem: (i) on the methodological side, we show that the $k$path coloring problem can be solved in polynomial time on graphs with bounded treewidth and we devise a simple polytime dynamic programming algorithm in this case (not relying on Courcelle's celebrated theorem); and (ii) on the empirical side, we provide computational evidences that the corresponding algorithm could be suitable for practice, by testing our algorithm on true instances obtained from an ongoing collaboration with Mentor Graphics. We finally compare this approach with integer programming on some pseudoindustrial instances. It suggests that dynamic programming cannot compete with integer programming when the treewidth is greater than three. While all our industrial instances exhibit such a small treewidth, this is not for granted that all future instances will also do, and this tend to advocate for integer programming approaches.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.11805
 Bibcode:
 2019arXiv190411805A
 Keywords:

 Computer Science  Discrete Mathematics