We consider a repulsion actuator located in an n-sided convex environment full of point particles. When the actuator is activated, all the particles move away from the actuator. We study the problem of gathering all the particles to a point. We give an O(n2) time algorithm to compute all the actuator locations that gather the particles to one point with one activation, and an O(n) time algorithm to find a single such actuator location if one exists. We then provide an O(n) time algorithm to place the optimal number of actuators whose sequential activation results in the gathering of the particles when such a placement exists.

Additional Metadata
Keywords Beacon attraction, Kernel, Phrases polygon
Persistent URL dx.doi.org/10.4230/LIPIcs.SWAT.2018.13
Conference 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
Citation
Bose, P, & Shermer, T.C. (Thomas C.). (2018). Gathering by repulsion. In Leibniz International Proceedings in Informatics, LIPIcs (pp. 131–1312). doi:10.4230/LIPIcs.SWAT.2018.13