Centroidal localization game
Bart{\l}omiej Bosek, Przemys{\l}aw Gordinowicz, Jaros{\l}aw Grytczuk,, Nicolas Nisse, Joanna Sok\'o{\l}, Ma{\l}gorzata \'Sleszy\'nska-Nowak

TL;DR
This paper introduces a new localization game where a moving entity is located using relative distance comparisons, providing bounds for various graph classes and establishing the problem's computational complexity.
Contribution
It generalizes the centroidal localization problem to a sequential probing setting, proving bounds for trees, outerplanar graphs, and Cartesian products, and shows NP-hardness for general graphs.
Findings
ta* (T) 2 for every tree T
ta* (G) pathwidth(G) + 1
The problem is NP-hard in general graphs
Abstract
One important problem in a network is to locate an (invisible) moving entity by using distance-detectors placed at strategical locations. For instance, the metric dimension of a graph is the minimum number of detectors placed in some vertices such that the vector of the distances between the detectors and the entity's location allows to uniquely determine . In a more realistic setting, instead of getting the exact distance information, given devices placed in , we get only relative distances between the entity's location and the devices (for every , it is provided whether , , or to ). The centroidal dimension of a graph is the minimum number of devices required to locate the entity in this setting. We consider the natural generalization…
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