# Discrete and Computational Geometry

@inproceedings{Leeuwen1998DiscreteAC, title={Discrete and Computational Geometry}, author={Jan van Leeuwen and Jin Akiyama and Mikio Kano and Masatsugu Urabe and Jan van Leeuwen}, booktitle={Lecture Notes in Computer Science}, year={1998} }

This talk surveys how geometric information can be effectively used for efficient algorithms with focus on clustering problems. Given a complete weighted graph G of n vertices, is there a partition of the vertex set into k disjoint subsets so that the maximum weight of an innercluster edge (whose two endpoints both belong to the same subset) is minimized. This problem is known to be NP-complete even for k = 3. The case of k = 2, that is, bipartition problem is solvable in polynomial time. On…

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Equal Area Polygons in Convex Bodies

- Mathematics, Computer ScienceIJCCGGT
- 2003

It is shown that for a convex quadrilateral K of area 1, there exist n internally disjoint triangles of equal area such that the sum of their areas is at least $\frac {4n}{4n+1}$.

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