10.3233/FI-2021-2075
Zarrabi, Mohammad Reza
Mohammad Reza
Zarrabi
Charkari, Nasrollah Moghaddam
Nasrollah Moghaddam
Charkari
Query-points visibility constraint minimum link paths in simple polygons
episciences.org
2021
Computer Science - Computational Geometry
contact@episciences.org
episciences.org
2021-08-24T11:44:26+02:00
2021-11-18T11:14:43+01:00
2021-11-18
eng
Journal article
https://fi.episciences.org/8386
arXiv:2004.02220
1875-8681
PDF
1
Fundamenta Informaticae ; Volume 182, Issue 3 ; 1875-8681
We study the query version of constrained minimum link paths between two
points inside a simple polygon $P$ with $n$ vertices such that there is at
least one point on the path, visible from a query point. The method is based on
partitioning $P$ into a number of faces of equal link distance from a point,
called a link-based shortest path map (SPM). Initially, we solve this problem
for two given points $s$, $t$ and a query point $q$. Then, the proposed
solution is extended to a general case for three arbitrary query points $s$,
$t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing
time. Extending this approach for the latter case, we develop an algorithm with
$O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between
$s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log
n)$, respectively, for the above two cases, where $m$ is the number of links.