The problem of compatible representatives
SIAM Journal on Discrete Mathematics
Perfect binary space partitions
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Optimal BSPs and rectilinear cartograms
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
An Algorithmic Study of Switch Graphs
Graph-Theoretic Concepts in Computer Science
Flattening fixed-angle chains is strongly NP-hard
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
GD'11 Proceedings of the 19th international conference on Graph Drawing
Folding equilateral plane graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
On d-regular schematization of embedded paths
Computational Geometry: Theory and Applications
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An optimal bsp for a set S of disjoint line segments in the plane is a bsp for S that produces the minimum number of cuts.We study optimal bsps for three classes of bsps, which differ in the splitting lines that can be used when partitioning a set of fragments in the recursive partitioning process: free bsps can use any splitting line, restricted bsps can only use splitting lines through pairs of fragment endpoints, and auto-partitions can only use splitting lines containing a fragment. We obtain the two following results: - It is np-hard to decide whether a given set of segments admits an auto-partition that does not make any cuts. - An optimal restricted bsp makes at most 2 times as many cuts as an optimal free bsp for the same set of segments.