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Pré-Publication, Document De Travail Année : 2022

The $k$-path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing

Résumé

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 `tree-like' 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 on-going collaboration with Mentor Graphics. We finally compare this approach with integer programming on some pseudo-industrial instances. It suggests that dynamic programming cannot compete with integer programming when the tree-width is greater than three. While all our industrial instances exhibit such a small tree-width, this is not for granted that all future instances will also do, and this tend to advocate for integer programming approaches.
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Dates et versions

hal-02148034 , version 1 (30-08-2022)

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Paternité - Pas d'utilisation commerciale

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Dehia Ait-Ferhat, Vincent Juliard, Gautier Stauffer, Andres Torres. The $k$-path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing. 2022. ⟨hal-02148034⟩

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