# Negative Instance for the Edge Patrolling Beacon Problem

@article{Abel2020NegativeIF, title={Negative Instance for the Edge Patrolling Beacon Problem}, author={Zachary Abel and H. Akitaya and E. Demaine and M. Demaine and Adam Hesterberg and Matias Korman and Jason S. Ku and J. Lynch}, journal={ArXiv}, year={2020}, volume={abs/2006.01202} }

Can an infinite-strength magnetic beacon always ``catch'' an iron ball, when the beacon is a point required to be remain nonstrictly outside a polygon, and the ball is a point always moving instantaneously and maximally toward the beacon subject to staying nonstrictly within the same polygon? Kouhestani and Rappaport [JCDCG 2017] gave an algorithm for determining whether a ball-capturing beacon strategy exists, while conjecturing that such a strategy always exists. We disprove this conjecture… Expand

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Chasing Puppies: Mobile Beacon Routing on Closed Curves

- Computer Science
- SoCG
- 2021

This paper solves an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others’ work on beacon-based routing and proves that the human can always catch the puppy in finite time. Expand

#### References

SHOWING 1-10 OF 10 REFERENCES

Efficient algorithms for beacon routing in polygons

- Computer Science
- 2017

The quality of a “successful” beacon attraction is considered, an upper bound of √ 2 is provided on the ratio between the length of the beacon trajectory and thelength of the geodesic distance in a simple polygon, and an O(n log n) time algorithm is introduced to solve the problem of computing the shortest beacon watchtower in a polygonal terrain. Expand

An Optimal Algorithm to Compute the Inverse Beacon Attraction Region

- Computer Science, Mathematics
- SoCG
- 2018

The total complexity of the inverse attraction region of a point in a simple polygon is linear, and a matching $\Omega(n\log n)$ lower bound for this task is proved in the algebraic computation tree model of computation, even if thepolygon is monotone. Expand

Combinatorics of Beacon-based Routing in Three Dimensions

- Computer Science, Mathematics
- LATIN
- 2018

It is shown that beacons are always sufficient and sometimes necessary to route between any pair of points in a given polyhedron $P$, where $m$ is the number of tetrahedra in a tetrahedral decomposition of $P$. Expand

A Combinatorial Bound for Beacon-based Routing in Orthogonal Polygons

- Computer Science, Mathematics
- CCCG
- 2015

Beacon attraction is a movement system whereby a robot (modeled as a point in 2D) moves in a free space so as to always locally minimize its Euclidean distance to an activated beacon (which is also a… Expand

Beacon-Based Algorithms for Geometric Routing

- Mathematics, Computer Science
- WADS
- 2013

A polynomial-time algorithm for routing from a point s to a point t using a discrete set of candidate beacons is established, as well as a 2-approximation and a PTAS for routing between beacons placed without restriction in P. Expand

Combinatorics of Beacon Routing and Coverage

- Computer Science
- CCCG
- 2013

In simple polygons with n vertices it is shown that ⌊ n 2 ⌋ − 1 beacons are sometimes necessary and always sufficient, and in polygONS with h holes it is established that ⊙ n 2⌊ −h−1 beaconsAre sometimes necessary while h− 1Beacons are always sufficient. Expand

Edge patrolling beacon

- In Abstracts from the 20th Japan Conference on Discrete and Computational Geometry, Graphs, and Games,
- 2017

Personal communication held after the presentation

- 2017

Beacon-based routing and coverage

- In Abstracts from the 21st Fall Workshop on Computational Geometry,
- 2011