Results on k-sets and j-facets via continuous motion
Proceedings of the fourteenth annual symposium on Computational geometry
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Tight Bounds for Connecting Sites Across Barriers
Discrete & Computational Geometry
Compatible geometric matchings
Computational Geometry: Theory and Applications
Approximate convex decomposition of polygons
Computational Geometry: Theory and Applications
Finding equitable convex partitions of points in a polygon efficiently
ACM Transactions on Algorithms (TALG)
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It is shown that for every finite set of disjoint convex polygonal obstacles in the plane, with a total of n vertices, the free space around the obstacles can be partitioned into open convex cells whose dual graph (defined below) is 2-edge connected. Intuitively, every edge of the dual graph corresponds to a pair of adjacent cells that are both incident to the same vertex. Aichholzer et al. recently conjectured that given an even number of line-segment obstacles, one can construct a convex partition by successively extending the segments along their supporting lines such that the dual graph is the union of two edge-disjoint spanning trees. Here we present a counterexamples to this conjecture, with n disjoint line segments for any n *** 15, such that the dual graph of any convex partition constructed by this method has a bridge edge, and thus the dual graph cannot be partitioned into two spanning trees.