TY - GEN
T1 - Subexponential-time and FPT algorithms for embedded flat clustered planarity
AU - Da Lozzo, Giordano
AU - Eppstein, David
AU - Goodrich, Michael T.
AU - Gupta, Siddharth
N1 - Publisher Copyright:
© 2018, Springer Nature Switzerland AG.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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 underlying graph and the number of disconnected clusters as parameters.
AB - 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 underlying graph and the number of disconnected clusters as parameters.
UR - http://www.scopus.com/inward/record.url?scp=85053454460&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-00256-5_10
DO - 10.1007/978-3-030-00256-5_10
M3 - Conference contribution
AN - SCOPUS:85053454460
SN - 9783030002558
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 111
EP - 124
BT - Graph-Theoretic Concepts in Computer Science - 44th International Workshop, WG 2018, Proceedings
A2 - Brandstädt, Andreas
A2 - Köhler, Ekkehard
A2 - Meer, Klaus
PB - Springer Verlag
T2 - 44th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2018
Y2 - 27 June 2018 through 29 June 2018
ER -