eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
51:1
51:16
10.4230/LIPIcs.ISAAC.2022.51
article
Partial and Simultaneous Transitive Orientations via Modular Decompositions
Münch, Miriam
1
https://orcid.org/0000-0002-6997-8774
Rutter, Ignaz
1
https://orcid.org/0000-0002-3794-4406
Stumpf, Peter
1
https://orcid.org/0000-0003-0531-9769
Faculty of Computer Science and Mathematics, Universität Passau, Germany
A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple input graphs that coincide on subgraphs shared by the input graphs. A common restriction is the sunflower case where the shared graph is the same for each pair of input graphs. These problems translate to the setting of comparability graphs where the representations correspond to transitive orientations of their edges. We use modular decompositions to improve the runtime for the orientation extension problem and the sunflower orientation problem to linear time. We apply these results to improve the runtime for the partial representation problem and the sunflower case of the simultaneous representation problem for permutation graphs to linear time. We also give the first efficient algorithms for these problems on circular permutation graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol248-isaac2022/LIPIcs.ISAAC.2022.51/LIPIcs.ISAAC.2022.51.pdf
representation extension
simultaneous representation
comparability graph
permutation graph
circular permutation graph
modular decomposition