Two points x, y inside a simple polygon P are said to be mutually link-2 visible if there exists the third point z ∈ P such that z is visible from both x and y. The polygon P is link-2 LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is link-2 visible from some point of the other boundary of P from t to s and vice versa. We give a characterization of link-2 LR-visibility polygons by generalizing the known result on LR-visibility polygons. A new idea is to extend the concepts of ray-shootings and components to those under notion of link-2 visibility. Then, we develop an O(n log n) time algorithm to determine whether a given polygon is link-2 LR-visible. Using the characterization of link-2 LR-visibility polygons, we further present an O(n log n) time algorithm for determining whether a polygonal region is searchable by a k-searcher, k ≥ 2. This improves upon the previous O(n2) time bound [9]. A polygonal region P is said to be searchable by a searcher if the searcher can detect (or see) an unpredictable intruder inside the region, no matter how fast the intruder moves. A k-searcher holds k flashlights and can see only along the rays of the flashlights emanating from his position.
Xuehou TAN
Tokai University
Bo JIANG
Dalian Maritime University
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copy
Xuehou TAN, Bo JIANG, "Characterizing Link-2 LR-Visibility Polygons and Related Problems" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 423-429, February 2019, doi: 10.1587/transfun.E102.A.423.
Abstract: Two points x, y inside a simple polygon P are said to be mutually link-2 visible if there exists the third point z ∈ P such that z is visible from both x and y. The polygon P is link-2 LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is link-2 visible from some point of the other boundary of P from t to s and vice versa. We give a characterization of link-2 LR-visibility polygons by generalizing the known result on LR-visibility polygons. A new idea is to extend the concepts of ray-shootings and components to those under notion of link-2 visibility. Then, we develop an O(n log n) time algorithm to determine whether a given polygon is link-2 LR-visible. Using the characterization of link-2 LR-visibility polygons, we further present an O(n log n) time algorithm for determining whether a polygonal region is searchable by a k-searcher, k ≥ 2. This improves upon the previous O(n2) time bound [9]. A polygonal region P is said to be searchable by a searcher if the searcher can detect (or see) an unpredictable intruder inside the region, no matter how fast the intruder moves. A k-searcher holds k flashlights and can see only along the rays of the flashlights emanating from his position.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.423/_p
Copy
@ARTICLE{e102-a_2_423,
author={Xuehou TAN, Bo JIANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Characterizing Link-2 LR-Visibility Polygons and Related Problems},
year={2019},
volume={E102-A},
number={2},
pages={423-429},
abstract={Two points x, y inside a simple polygon P are said to be mutually link-2 visible if there exists the third point z ∈ P such that z is visible from both x and y. The polygon P is link-2 LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is link-2 visible from some point of the other boundary of P from t to s and vice versa. We give a characterization of link-2 LR-visibility polygons by generalizing the known result on LR-visibility polygons. A new idea is to extend the concepts of ray-shootings and components to those under notion of link-2 visibility. Then, we develop an O(n log n) time algorithm to determine whether a given polygon is link-2 LR-visible. Using the characterization of link-2 LR-visibility polygons, we further present an O(n log n) time algorithm for determining whether a polygonal region is searchable by a k-searcher, k ≥ 2. This improves upon the previous O(n2) time bound [9]. A polygonal region P is said to be searchable by a searcher if the searcher can detect (or see) an unpredictable intruder inside the region, no matter how fast the intruder moves. A k-searcher holds k flashlights and can see only along the rays of the flashlights emanating from his position.},
keywords={},
doi={10.1587/transfun.E102.A.423},
ISSN={1745-1337},
month={February},}
Copy
TY - JOUR
TI - Characterizing Link-2 LR-Visibility Polygons and Related Problems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 423
EP - 429
AU - Xuehou TAN
AU - Bo JIANG
PY - 2019
DO - 10.1587/transfun.E102.A.423
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2019
AB - Two points x, y inside a simple polygon P are said to be mutually link-2 visible if there exists the third point z ∈ P such that z is visible from both x and y. The polygon P is link-2 LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is link-2 visible from some point of the other boundary of P from t to s and vice versa. We give a characterization of link-2 LR-visibility polygons by generalizing the known result on LR-visibility polygons. A new idea is to extend the concepts of ray-shootings and components to those under notion of link-2 visibility. Then, we develop an O(n log n) time algorithm to determine whether a given polygon is link-2 LR-visible. Using the characterization of link-2 LR-visibility polygons, we further present an O(n log n) time algorithm for determining whether a polygonal region is searchable by a k-searcher, k ≥ 2. This improves upon the previous O(n2) time bound [9]. A polygonal region P is said to be searchable by a searcher if the searcher can detect (or see) an unpredictable intruder inside the region, no matter how fast the intruder moves. A k-searcher holds k flashlights and can see only along the rays of the flashlights emanating from his position.
ER -