Proximity problems on line segments spanned by points
Computational Geometry: Theory and Applications
On the all-farthest-segments problem for a planar set of points
Information Processing Letters
Farthest line segment Voronoi diagrams
Information Processing Letters
On the number of tetrahedra with minimum, unit, and distinct volumes in three-space
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An O(nlogn) algorithm for the all-farthest-segments problem for a planar set of points
Information Processing Letters
Extremal problems on triangle areas in two and three dimensions
Proceedings of the twenty-fourth annual symposium on Computational geometry
Extremal point queries with lines and line segments and related problems
Computational Geometry: Theory and Applications
| Hi-index | 0.89 |
Given a set S of n points in R^3 we consider finding the farthest line segment spanned by S from a query point q given as part of the input, and finding the minimum and maximum area triangles spanned by S. For the farthest line segment problem we give an O(nlogn) time, O(n) space algorithm, matching the time and space complexities of the planar version. The algorithm is optimal in the algebraic decision tree model. We further prove that the minimum area triangle spanned by S can be found in O(n^2^.^4log^O^(^1^)n) time and space, and the maximum area triangle spanned by S can be found in O(h^2^.^4log^O^(^1^)h+nlogn) time and O(h^2^.^4log^O^(^1^)h+n) space, where h is the number of vertices of the convex hull of S (h=n in the worst case).