Subexponential-Time and FPT Algorithms for Embedded Flat Clustered Planarity

(left) Partial saturation of c-graph $H$ by
means of candidate saturating edges lying in
the interior of cycle $\rho$.
(right) Cycle-star $S^-$ representing the
cluster-connectivity in the interior of $\rho$


The C-Planarity problem asks for a drawing of a clustered graph, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edge- edge crossings, no region-region crossings, and no unnecessary edge-region crossings. We study C-Planarity for embedded flat clustered graphs, graphs with a fixed combinatorial embedding whose clusters partition the vertex set. Our main result is a subexponential-time algorithm to test C-Planarity for these graphs when their face size is bounded. Furthermore, we consider a variation of the notion of embedded tree decomposition in which, for each face, including the outer face, there is a bag that contains every vertex of the face. We show that C-Planarity is fixed-parameter tractable with the embedded-width of the the underlying graph and the number of disconnected clusters as parameters.

In 44th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2018)
Giordano Da Lozzo
Assistant Professor (RTDb)

My research interests are in Algorithm Engineering and Complexity, focused in particular on the theoretical and algorithmic challenges arising from the visualization of graphs.