Triangles Cover Triangle (Geometric Covering Problems)

Description

Given a set of triangles in the plane, does their union contain another given triangle?

Related Problems

Related: Strips Cover Box, Hole in Union, 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
Hole in Union	if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$	1995	https://doi.org/10.1016/0925-7721(95)00022-2	link
Triangle Measure	if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$	1995	https://doi.org/10.1016/0925-7721(95)00022-2	link
Visible 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/10.1016/0925-7721(95)00022-2	link
3D Motion Planning	if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$	1995	https://doi.org/10.1016/0925-7721(95)00022-2	link

Reductions FROM Problem

Problem	Implication	Year	Citation	Reduction
Strips Cover Box	if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$	1995	https://doi.org/10.1016/0925-7721(95)00022-2	link
Hole in Union	if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$	1995	https://doi.org/10.1016/0925-7721(95)00022-2	link
Visible 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/10.1016/0925-7721(95)00022-2	link