New lower bounds on the cutwidth of graphs
Résumé
Cutwidth is a parameter used in many layout problems. Determining the cutwidth of a graph is an NP-complete problem, but it is possible to design e!cient branch-and-bound algorithms if good lower bounds are available for cutting branches during exploration. Knowing how to quickly evaluate good bounds in each node of the search tree is therefore crucial.
In this article, we give new lower bounds based on di"erent graph density parameters such as the minimum, the average and the maximum average degree. Our main result is a new bound using the notion of tra!c grooming on a path network, which appear to be in many cases better than bounds in the literature. Furthermore, the bound based on grooming can be computed quickly, in O(log n) time, and so is of interest to design faster branch-andbound algorithms. Through extensive experiments, we show that this bound behaves very well compared to other bounds. Furthermore, we show how to obtain even better results when combining it with heuristics for finding dense subgraphs.
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