Geodesic
Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth
Journal of Graph Algorithms and Applications, Tome 24 (2020) no. 3, pp. 461-482.

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Many combinatorial problems can be solved in time $\mathcal{O}^*(c^{\mathrm{tw}})$ on graphs of treewidth $\mathrm{tw}$, for a problem-specific constant $c$. In several cases, matching upper and lower bounds on $c$ are known based on the Strong Exponential Time Hypothesis (SETH). In this paper we investigate the complexity of solving problems on graphs of bounded cutwidth, a graph parameter that takes larger values than treewidth. We strengthen earlier treewidth-based lower bounds to show that, assuming SETH, $\rm{I{\small NDEPENDENT}~S{\small ET}}$ cannot be solved in $O^*((2-\varepsilon)^{\mathrm{ctw}})$ time, and $\rm{D{\small OMINATING}~S{\small ET}}$ cannot be solved in $O^*((3-\varepsilon)^{\mathrm{ctw}})$ time. By designing a new crossover gadget, we extend these lower bounds even to planar graphs of bounded cutwidth or treewidth. Hence planarity does not help when solving $\rm{I{\small NDEPENDENT}~S{\small ET}}$ or $\rm{D{\small OMINATING}~S{\small ET}}$ on graphs of bounded width. This sharply contrasts the fact that in many settings, planarity allows problems to be solved much more efficiently.
DOI : 10.7155/jgaa.00542
Keywords: planarization, dominating set, cutwidth, lower bounds, strong exponential time hypothesis 
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Bas van Geffen; Bart Jansen; Arnoud de Kroon; Rolf Morel. Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth. Journal of Graph Algorithms and Applications, Tome 24 (2020) no. 3, pp. 461-482. doi : 10.7155/jgaa.00542. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00542/

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