Polygon triangulation: efficiency and minimality
Journal of Algorithms
Efficient algorithms for geometric graph search problems
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Algorithms for some intersection graphs
Proceedings of the 17th Symposium of Research Institute of Electric Communication on Graph Theory and Algorithms
Decomposing a polygon into its convex parts
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Minimum K-partitioning of rectilinear polygons
Journal of Symbolic Computation
A single-exponential upper bound for finding shortest paths in three dimensions
Journal of the ACM (JACM)
Vertex correspondence between polygons in different applications
Machine Graphics & Vision International Journal
An innovative Steiner tree based approach for polygon partitioning
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
Efficiently implementing maximum independent set algorithms on circle graphs
Journal of Experimental Algorithmics (JEA)
Digitization scheme that assures faithful reconstruction of plane figures
Pattern Recognition
Planar subset of multi-terminal nets
Integration, the VLSI Journal
Scaling of plane figures that assures faithful digitization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Algorithms and theory of computation handbook
ACCORD: with approximate covering of convex orthogonal decomposition
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Approximate partitioning of 2D objects into orthogonally convex components
Computer Vision and Image Understanding
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The problem of partitioning a polygonal region into a minimum number of trapezoids with two horizontal sides is discussed. A triangle with a horizontal side is considered to be a trapezoid with two horizontal sides one of which is degenerate. First, a method of achieving a minimum partition is presented. The number M* of the trapezoids in the minimum partition of a polygonal region P is shown to be M* = n + w - h - d - 1, where n, w, and h are the number of vertices, windows (holes), and horizontal edges of P, respectively, and d is the cardinality of a maximum independent set of the straight-lines-in-the-plane graph associated with P. Next, this problem is shown to be polynomially equivalent to the problem of finding a maximum independent set of a straight-lines-in-the-plane graph, and consequently, it is shown to be NP-complete. However, for a polygonal region without windows, an O(n2)-time algorithm for partitioning it into a minimum number of trapezoids is presented. Finally, an O(n log n)-time approximation algorithm with the performance bound 3 is presented.