Drawing graphs
Schematization of road networks
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Rendering effective route maps: improving usability through generalization
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Line Simplification with Restricted Orientations
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
A Layout Adjustment Problem for Disjoint Rectangles Preserving Orthogonal Order
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Sketch-Driven Orthogonal Graph Drawing
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Speeding-up linear programming using fast matrix multiplication
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Path simplification for metro map layout
GD'06 Proceedings of the 14th international conference on Graph drawing
Automatic generation of destination maps
ACM SIGGRAPH Asia 2010 papers
Optimal binary space partitions in the plane
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
On d-regular schematization of embedded paths
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming
IEEE Transactions on Visualization and Computer Graphics
A new method for subdivision simplification with applications to urban-area generalization
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Stress majorization with orthogonal ordering constraints
GD'05 Proceedings of the 13th international conference on Graph Drawing
Homotopic rectilinear routing with few links and thick edges
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Path schematization for route sketches
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
GD'12 Proceedings of the 20th international conference on Graph Drawing
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Motivated by drawing route sketches, we consider the d-regular path schematization problem. For this problem we are given an embedded path P (e.g., a route in a road network) and a positive integer d. The goal is to find a d-schematized embedding of P in which the orthogonal order of all vertices in the input is preserved and in which every edge has a direction that is an integer multiple of (90/d)^o. We show that deciding whether a path can be d-schematized is NP-complete for any positive integer d. Despite the NP-hardness of the problem we still want to be able to generate route sketches and thus need to solve the d-regular path schematization problem. We explore two different algorithmic approaches, both of which consider two additional quality constraints: We require that every edge is drawn with a user-specified minimum length and we want to maximize the number of edges that are drawn with their preferred direction. The first algorithmic approach restricts the input paths to be axis-monotone. We show that there exists a polynomial-time algorithm that solves the d-regular path schematization problem for this restricted class of embedded paths. We extend this approach by a heuristic such that it can handle arbitrary simple paths. However, for the second step we cannot guarantee that the orthogonal order of the input embedding is maintained. The second approach is a formulation of the d-regular path schematization problem as a mixed integer linear program. Finally, we give an experimental evaluation which shows that both approaches generate reasonable route sketches for real-world data.