TY - GEN
T1 - Parameterized Approaches to Orthogonal Compaction
AU - Didimo, Walter
AU - Gupta, Siddharth
AU - Kindermann, Philipp
AU - Liotta, Giuseppe
AU - Wolff, Alexander
AU - Zehavi, Meirav
N1 - Funding Information:
Keywords: Orthogonal graph drawing · Orthogonal representation · Compaction · Parameterized complexity This research was initiated at Dagstuhl Seminar 21293: Parameterized Complexity in Graph Drawing. Work partially supported by: (i) Dep. of Engineering, Perugia University, grant RICBA21LG: Algoritmi, modelli e sistemi per la rappresentazione visuale di reti, (ii) Engineering and Physical Sciences Research Council (EPSRC) grant EP/V007793/1, (vi) European Research Council (ERC) grant termed PARAPATH.
Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has minimum area among all grid drawings that adhere to the given orthogonal representation. This problem is called orthogonal compaction (OC) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al. 2022]. We investigate the complexity of OC with respect to several parameters. Among others, we show that OC is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the OC problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.
AB - Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has minimum area among all grid drawings that adhere to the given orthogonal representation. This problem is called orthogonal compaction (OC) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al. 2022]. We investigate the complexity of OC with respect to several parameters. Among others, we show that OC is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the OC problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.
KW - Orthogonal graph drawing
KW - Orthogonal representation
KW - Compaction
KW - Parameterized complexity
UR - http://www.scopus.com/inward/record.url?scp=85146693238&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-23101-8_8
DO - 10.1007/978-3-031-23101-8_8
M3 - Conference contribution
SN - 9783031231001
VL - 13878
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 111
EP - 125
BT - SOFSEM 2023
A2 - Gasieniec, Leszek
PB - Springer Science and Business Media Deutschland GmbH
CY - Cham
T2 - 48th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2023
Y2 - 15 January 2023 through 18 January 2023
ER -