Clique-Width of Point Configurations
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Combinatorial Theory, Ser B |
| MU Faculty or unit | |
| Citation | |
| Web | |
| Doi | http://dx.doi.org/10.1016/j.jctb.2021.09.001 |
| Keywords | point configuration; order type; fixed-parameter tractability; relational structure; clique-width |
| Description | While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of clique-width to geometric point configurations represented by their order type. We study basic properties of this clique-width notion, and show that it is aligned with the general concept of clique-width of relational structures by Blumensath and Courcelle (2006). We also relate the new notion to monadic second-order logic of point configurations. As an application, we provide several linear FPT time algorithms for geometric point problems which are NP-hard in general, in the special case that the input point set is of bounded clique-width and the clique-width expression is also given. |
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