Finding Paths in Grids with Forbidden Transitions

Kanté, Mamadou Moustapha; Moataz, Fatima Zahra; Momège, Benjamin; Nisse, Nicolas

doi:10.1007/978-3-662-53174-7_12

Cited by 12 publications

(3 citation statements)

References 21 publications

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“…Here an instance is then a graph G and a set of conflicts. Obtaining a solution without conflict is hard in general for many graph problems, as it is shown in these papers [4,5,6,9,10,11,12,13,14,15,17].…”

Section: Obligationsmentioning

confidence: 99%

Graph Problems with Obligations

Cornet

Laforest

2018

Combinatorial Optimization and Applications

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Section: Obligationsmentioning

confidence: 99%

Graph Problems with Obligations

Cornet

Laforest

2018

Combinatorial Optimization and Applications

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“…Similarly, many known results about forbidden-transition graphs are proofs of NP-completeness of problems that are polynomially solvable on standard graphs (e.g. [1], [7], [18], [27], [28], [34], [35], [49]).…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Routing Problems in Forbidden-Transition Graphs and Edge-Colored Graphs

Bellitto

Okrasa

et al. 2022

Algorithmica

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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. A widely-studied special case are edge-colored graphs, where a compatible walk is forbidden to take two edges of the same color in a row. We initiate the study of fundamental problems on finding paths, cycles and walks in forbidden-transition graphs 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 for finding a compatible Hamiltonian cycle in the edge-colored graph setting.

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Section: Introductionmentioning

confidence: 99%

The Complexity of Connectivity Problems in Forbidden-Transition Graphs and Edge-Colored Graphs

Bellitto,

Li,

Okrasa

et al. 2020

Preprint

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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. Forbiddentransition 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 edgecolored graphs is one of the most studied special cases of compatible walks in forbidden-transition graphs.

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Finding Paths in Grids with Forbidden Transitions

Cited by 12 publications

References 21 publications

Graph Problems with Obligations

Graph Problems with Obligations

The Complexity of Routing Problems in Forbidden-Transition Graphs and Edge-Colored Graphs

The Complexity of Connectivity Problems in Forbidden-Transition Graphs and Edge-Colored Graphs

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