eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
24:1
24:15
10.4230/LIPIcs.SoCG.2020.24
article
Geometric Secluded Paths and Planar Satisfiability
Buchin, Kevin
1
Polishchuk, Valentin
2
Sedov, Leonid
2
Voronov, Roman
3
Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Communications and Transport Systems, ITN, Linköping University, Sweden
Institute of Mathematics and Information Technologies, Petrozavodsk State University, Russia
We consider paths with low exposure to a 2D polygonal domain, i.e., paths which are seen as little as possible; we differentiate between integral exposure (when we care about how long the path sees every point of the domain) and 0/1 exposure (just counting whether a point is seen by the path or not). For the integral exposure, we give a PTAS for finding the minimum-exposure path between two given points in the domain; for the 0/1 version, we prove that in a simple polygon the shortest path has the minimum exposure, while in domains with holes the problem becomes NP-hard. We also highlight connections of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol164-socg2020/LIPIcs.SoCG.2020.24/LIPIcs.SoCG.2020.24.pdf
Visibility
Route planning
Security/privacy
Planar satisfiability