Searching for the kernel of a polygon—a competitive strategy
Proceedings of the eleventh annual symposium on Computational geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
New competitive strategies for searching in unknown star-shaped polygons
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Position-independent near optimal searching and on-line recognition in star polygons
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
| Hi-index | 0.00 |
We consider all planar oriented curves that have the following property depending on a fixed angle ϕ. For each point B on the curve, the rest of the curve lies inside a wedge of angle ϕ with apex in B. This property restrains the curve's meandering, and for ϕ ≤ π/2 this means that a point running along the curve always gets closer to all points on the remaining part. For all ϕ c(ϕ) for the length of such a curve, divided by the distance between its endpoints, and prove this bound to be tight. A main step is in proving that the curve's length cannot exceed the perimeter of its convex hull, divided by 1 + cos ϕ.