A VLSI Solution to the Vertical Segment Visibility Problem
IEEE Transactions on Computers
Discrete Mathematics
Journal of Algorithms
Counting linear extensions is #P-complete
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Characterizing bar line-of-sight graphs
SCG '85 Proceedings of the first annual symposium on Computational geometry
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Weighted Visibility Graphs of Bars and Related Flow Problems (Extended Abstract)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Universal 3-Dimensional Visibility Representations for Graphs
GD '95 Proceedings of the Symposium on Graph Drawing
New Results on a Visibility Representation of Graphs in 3D
GD '95 Proceedings of the Symposium on Graph Drawing
On Representations of Some Thickness-Two Graphs
GD '95 Proceedings of the Symposium on Graph Drawing
Regular Edge Labelings and Drawings of Planar Graphs
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Rectangle-Visibility Representations of Bipartite Graphs
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
On Rectangle Visibility Graphs. III. External Visibility and Complexity
Proceedings of the 8th Canadian Conference on Computational Geometry
Bar-representable visibility graphs and a related network flow problem
Bar-representable visibility graphs and a related network flow problem
Journal of Computer and System Sciences
GD'05 Proceedings of the 13th international conference on Graph Drawing
Unit bar-visibility layouts of triangulated polygons
GD'04 Proceedings of the 12th international conference on Graph Drawing
Unsolved problems in visibility graphs of points, segments, and polygons
ACM Computing Surveys (CSUR)
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Non-overlapping axis-aligned rectangles in the plane define visibility graphs in which vertices are associated with rectangles and edges with visibility in either the horizontal or vertical direction. The recognition problem for such graphs is known to be NP-complete. This paper introduces the topological rectangle visibility graph.We give a polynomial time algorithm for recognizing such a graph and for constructing, when possible, a realizing set of rectangles on the unit grid. The bounding box of these rectangles has optimum length in each dimension. The algorithm provides a compaction tool: given a set of rectangles, one computes its associated graph, and runs the algorithm to get a compact set of rectangles with the same visibility properties.