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The search-type problem of evacuating 2 robots in the wireless model from the(Euclidean) unit disk was first introduced and studied by Czyzowicz et al.[DISC'2014]. Since then, the problem has seen a long list of follow-up resultspertaining to variations as well as to upper and lower bound improvements. Allestablished results in the area study this 2-dimensional search-type problem inthe Euclidean metric space where the search space, i.e. the unit disk, enjoyssignificant (metric) symmetries.  We initiate and study the problem of evacuating 2 robots in the wirelessmodel from $\ell_p$ unit disks, $p \in [1,\infty)$, where in particular robots'moves are measured in the underlying metric space. To the best of ourknowledge, this is the first study of a search-type problem with mobile agentsin more general metric spaces. The problem is particularly challenging sinceeven the circumference of the $\ell_p$ unit disks have been the subject oftechnical studies. In our main result, and after identifying and utilizing thevery few symmetries of $\ell_p$ unit disks, we design \emph{optimal evacuationalgorithms} that vary with $p$. Our main technical contributions are two-fold.First, in our upper bound results, we provide (nearly) closed formulae for theworst case cost of our algorithms. Second, and most importantly, our lowerbounds' arguments reduce to a novel observation in convex geometry whichanalyzes trade-offs between arc and chord lengths of $\ell_p$ unit disks as theendpoints of the arcs (chords) change position around the perimeter of thedisk, which we believe is interesting in its own right. Part of our argumentpertaining to the latter property relies on a computer assisted numericalverification that can be done for non-extreme values of $p$.

Evacuating from ell_p Unit Disks in the Wireless Model