On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
SIAM Journal on Computing
A better heuristic for orthogonal graph drawings
Computational Geometry: Theory and Applications
Spirality and Optimal Orthogonal Drawings
SIAM Journal on Computing
Computing Orthogonal Drawings with the Minimum Number of Bends
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
A New Minimum Cost Flow Algorithm with Applications to Graph Drawing
GD '96 Proceedings of the Symposium on Graph Drawing
A Linear Algorithm for Optimal Orthogonal Drawings of Triconnected Cubic Plane Graphs
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Improved Algorithms and Bounds for Orthogonal Drawings
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Minimum depth graph embeddings and quality of the drawings: an experimental analysis
GD'05 Proceedings of the 13th international conference on Graph Drawing
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This paper addresses the classical graph drawing problem of designing an algorithm that computes an orthogonal representation with the minimum number of bends, by considering all possible planar embeddings of the graph. While the general problem has been shown to be NP-complete [7], polynomial time algorithms have been devised for graphs whose vertex degree is at most three [5]. We show the first algorithm whose time complexity is exponential only in the number of vertices of degree four of the input graph. This settles a problem left as open in [5]. Our algorithm is further extended to handle graphs with vertices of degree higher than four. The analysis of the algorithm is supported by several experiments on the structure of a large set of input graphs.