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 -