Clique-Based Separators for Geometric Intersection Graphs

Abstract Let F be a set of n objects in the plane and let $$\mathcal {G}^{\times }(F)$$ G × ( F ) its intersection graph. A balanced clique-based separator is {\mathcal {S}}$$ S consisting cliques whose removal partitions into components size at most $$\delta n$$ δ n , for some fixed constant <1$$ < 1 . The weight defined as $$\sum _{C\in \mathcal {S}}}\log (|C|+1)$$ ∑ C ∈ log | + Recently De Berg et al. (SIAM J. Comput. 49: 1291-1331. 2020) proved that if S consists convex fat objects, then admits $$O(\sqrt{n})$$ O We extend this result several directions, obtaining following results. (i) Map graphs admit which tight worst case. (ii) Intersection pseudo-disks $$O(n^{2/3}\log n)$$ 2 / 3 If are polygonal total complexity O ( ) improves to $$O(\sqrt{n}\log (iii) geodesic disks inside simple polygon (iv) Visibility-restricted unit-disk domain with r reflex vertices $$O(\sqrt{n}+r\log (n/r))$$ r These results immediately imply sub-exponential algorithms Maximum Independent Set (and, hence, Vertex Cover ), Feedback q - Coloring these graph classes.