TY - GEN
T1 - The complexity of connectivity problems in forbidden-transition graphs and edge-colored graphs
AU - Bellitto, Thomas
AU - Li, Shaohua
AU - Okrasa, Karolina
AU - Pilipczuk, Marcin
AU - Sorge, Manuel
N1 - Publisher Copyright:
© Thomas Bellitto, Shaohua Li, Karolina Okrasa, Marcin Pilipczuk, and Manuel Sorge.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs of consecutive edges on the walk are permitted. Forbidden-transition graphs and related models have found applications in a variety of fields, such as routing in optical telecommunication networks, road networks, and bio-informatics. We initiate the study of fundamental connectivity problems from the point of view of parameterized complexity, including an in-depth study of tractability with regards to various graph-width parameters. Among several results, we prove that finding a simple compatible path between given endpoints in a forbidden-transition graph is W[1]-hard when parameterized by the vertex-deletion distance to a linear forest (so it is also hard when parameterized by pathwidth or treewidth). On the other hand, we show an algebraic trick that yields tractability when parameterized by treewidth of finding a properly colored Hamiltonian cycle in an edge-colored graph; properly colored walks in edge-colored graphs is one of the most studied special cases of compatible walks in forbidden-transition graphs.
AB - The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs of consecutive edges on the walk are permitted. Forbidden-transition graphs and related models have found applications in a variety of fields, such as routing in optical telecommunication networks, road networks, and bio-informatics. We initiate the study of fundamental connectivity problems from the point of view of parameterized complexity, including an in-depth study of tractability with regards to various graph-width parameters. Among several results, we prove that finding a simple compatible path between given endpoints in a forbidden-transition graph is W[1]-hard when parameterized by the vertex-deletion distance to a linear forest (so it is also hard when parameterized by pathwidth or treewidth). On the other hand, we show an algebraic trick that yields tractability when parameterized by treewidth of finding a properly colored Hamiltonian cycle in an edge-colored graph; properly colored walks in edge-colored graphs is one of the most studied special cases of compatible walks in forbidden-transition graphs.
KW - Fixed-parameter tractability
KW - Graph algorithms
KW - Parameterized complexity
UR - http://www.scopus.com/inward/record.url?scp=85100927105&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2020.59
DO - 10.4230/LIPIcs.ISAAC.2020.59
M3 - Conference contribution
AN - SCOPUS:85100927105
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 591
EP - 5915
BT - 31st International Symposium on Algorithms and Computation, ISAAC 2020
A2 - Cao, Yixin
A2 - Cheng, Siu-Wing
A2 - Li, Minming
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 31st International Symposium on Algorithms and Computation, ISAAC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -
