Hole in Union (Geometric Covering Problems)
Revision as of 10:29, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Hole in Union (Geometric Covering Problems)}} == Description == Given a set of triangles in the plane, does their union contain a hole? == Related Problems == Related: Strips Cover Box, Triangles Cover Triangle, Triangle Measure, Point Covering, Max-Weight Rectangle, Weighted Depth == Parameters == <pre>n: number of triangles</pre> == Table of Algorithms == Currently no algorithms in our database for the given problem. =...")
Description
Given a set of triangles in the plane, does their union contain a hole?
Related Problems
Related: Strips Cover Box, Triangles Cover Triangle, Triangle Measure, Point Covering, Max-Weight Rectangle, Weighted Depth
Parameters
n: number of triangles
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions TO Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Triangles Cover Triangle | if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$ |
1995 | https://doi-org.ezproxy.canberra.edu.au/10.1016/0925-7721(95)00022-2 | link |
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Triangles Cover Triangle | if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$ |
1995 | https://doi-org.ezproxy.canberra.edu.au/10.1016/0925-7721(95)00022-2 | link |