9 papers · 1 filter
On the Spanning Ratio of the Greedy Triangulation for Convex Point Sets
Prosenjit Bose, Jean Lou de Carufel, Anil Maheshwari +3
The greedy triangulation of a finite planar point set is obtained by considering all segments in nondecreasing order of length and inserting each segment that does not cross an ear…
Closest Pair Queries in Vertical Slabs and Tight Bounds on the Number of Possible Answers
Ahmad Biniaz, Prosenjit Bose, Chaeyoon Chung +6
Let be a set of points in , where is a constant, and let be a sequence of vertical hyperplanes that are sorted by their fi…
On geodesic disks enclosing many points
Prosenjit Bose, Guillermo Esteban, David Orden +2
Let be the largest number such that for every set of points in a polygon~, there always exist two points , where every geodesic disk contai…
Computational aspects of disks enclosing many points
Prosenjit Bose, Guillermo Esteban, Tyler Tuttle
Let be a set of points in the plane. We present several different algorithms for finding a pair of points in such that any disk that contains that pair must contain at…
Noncrossing Longest Paths and Cycles
Greg Aloupis, Ahmad Biniaz, Prosenjit Bose +7
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout. Short…
An Improved Bound for Plane Covering Paths
Hugo A. Akitaya, Greg Aloupis, Ahmad Biniaz +8
A covering path for a finite set of points in the plane is a polygonal path such that every point of lies on a segment of the path. The vertices of the path need not be at…