Polygon-Constrained Motion Planning Problems

Davide Bilò, Yann Disser, Luciano Gualà, Matús Mihalák, Guido Proietti, Peter Widmayer

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

We consider the following class of polygon-constrained motion planning problems: given a set of kk centrally controlled mobile agents (say pebbles) initially sitting on the vertices of an nn-vertex simple polygon pp, we study how to plan their vertex-to-vertex motion in order to reach with a minimum (either maximum or total) movement (either in terms of number of hops or euclidean distance) a final placement enjoying a given requirement. In particular, we focus on final configurations aiming at establishing some sort of visual connectivity among the pebbles, which in turn allows for wireless and optical intercommunication. Therefore, after analyzing the notable (and computationally tractable) case of gathering the pebbles at a single vertex (i.e., the so-called rendez-vous), we face the problems induced by the requirement that pebbles have eventually to be placed at: (i) a set of vertices that form a connected subgraph of the visibility graph induced by pp, say g(p)g(p) (connectivity), and (ii) a set of vertices that form a clique of g(p)g(p) (clique-connectivity). We will show that these two problems are actually hard to approximate, even for the seemingly simpler case in which the hop distance is considered.
Original languageEnglish
Title of host publicationProceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)
PublisherSpringer Verlag
Pages67-82
Number of pages16
DOIs
Publication statusPublished - 2013

Publication series

SeriesLecture Notes in Computer Science
Volume8243

Cite this

Bilò, D., Disser, Y., Gualà, L., Mihalák, M., Proietti, G., & Widmayer, P. (2013). Polygon-Constrained Motion Planning Problems. In Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS) (pp. 67-82). Springer Verlag. Lecture Notes in Computer Science, Vol.. 8243 https://doi.org/10.1007/978-3-642-45346-5_6