Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard

This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedd...

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Detalles Bibliográficos
Autores: Garrido Vizuete, María de los Angeles, Márquez Pérez, Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1997
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/33425
Acceso en línea:http://hdl.handle.net/11441/33425
https://doi.org/10.1007/3-540-63938-1_56
Access Level:acceso abierto
Palabra clave:Theory of Computation
Discrete Mathematics
Computer-Aided Engineering (CAD, CAE) and Design
Discrete Mathematics in Computer Science
Combinatorics
Algorithm Analysis and Problem Complexity
Descripción
Sumario:This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedding essentially equivalent to a given embedding, and that given a graph, testing if there exists a surface such that the graph admits a rectilinear embedding in that surface are NP-complete problems and hence the corresponding optimization problems are NP-hard.