episciences.org_8386_1642655423
1642655423
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Fundamenta Informaticae
1875-8681
11
18
2021
Volume 182, Issue 3
Query-points visibility constraint minimum link paths in simple polygons
Mohammad Reza
Zarrabi
Nasrollah Moghaddam
Charkari
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.
11
18
2021
8386
arXiv:2004.02220
10.3233/FI-2021-2075
https://fi.episciences.org/8386