Journal ArticleDOI
Map graphs
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An NP characterization is given for planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires).Abstract:
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, derive some consequences regarding sparsity and coloring, and survey some algorithmic results.read more
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Book ChapterDOI
Qualitative spatial representation and reasoning
Anthony G. Cohn,Jochen Renz +1 more
TL;DR: The challenge of qualitative spatial reasoning (QSR) is to provide calculi that allow a machine to represent and reason with spatial entities without resort to the traditional quantitative techniques prevalent in, for example, computer graphics or computer vision communities.
Journal ArticleDOI
The Bidimensionality Theory and Its Algorithmic Applications 1
TL;DR: The foundation of this work is the topological theory of drawings of graphs on surfaces and the results regarding the relation of the size of the largest grid minor in terms of treewidth in bounded-genus graphs and more generally in graphs excluding a fixed graph H as a minor.
Journal ArticleDOI
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
TL;DR: The approach builds on the seminal results of Robertson and Seymour on Graph Minors, and as a result is much more powerful than the previous machinery of Alber et al. for exponential speedup on planar graphs.
Journal ArticleDOI
Minimal Obstructions for 1-Immersions and Hardness of 1-Planarity Testing
Vladimir P. Korzhik,Bojan Mohar +1 more
TL;DR: It is proved that for every integer , there are at least nonisomorphic minimal non-1-planar graphs of order n and that testing 1-planarity is NP-complete.
Journal ArticleDOI
An annotated bibliography on 1-planarity
TL;DR: The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity as discussed by the authors, and it has driven increasing attention in the areas of graph theory, graph algorithms, graph drawing, and computational geometry.
References
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Journal ArticleDOI
Maintaining knowledge about temporal intervals
TL;DR: In this paper, an interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation, which is notable in offering a delicate balance between time and space.
Journal ArticleDOI
Efficient Planarity Testing
TL;DR: An efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane is described, which used depth-first search and has time and space bounds.
Journal ArticleDOI
String graphs. II.: Recognizing string graphs is NP-hard
TL;DR: It is proved that recognizing string graphs and some related problems are NP-hard.
Proceedings Article
Topological inference
TL;DR: In this paper, the authors study the computational problems involved in developing such an inference system and point out that the problem has two distinct components that interact in rather complex ways: relational consistency, and planarity.
Proceedings ArticleDOI
Recognizing string graphs in NP
TL;DR: It is shown that the recognition problem for string graphs is in NP, and therefore NP-complete, since Kratochvíl showed that the Recognition problem is NP-hard.