Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
On a matching problem in the plane
Discrete Mathematics
Matching colored points in the plane: some new results
Computational Geometry: Theory and Applications
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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It is shown that any two-colored set of n points in general position in the plane can be partitioned into at most ⌈n+1/2⌉ monochromatic subsets, whose convex hulls are pairwise disjoint. This bound cannot be improved in general. We present an O(n log n) time algorithm for constructing a partition into fewer parts, if the coloring is unbalanced, i.e., the sizes of the two color classes differ by more than one. The analogous question for k-colored point sets (k 2) and its higher dimensional variant are also considered.