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We study the sample placement and shortest tour problem for robots taskedwith mapping environmental phenomena modeled as stationary random fields. Theobjective is to minimize the resources used (samples or tour length) whileguaranteeing estimation accuracy. We give approximation algorithms for bothproblems in convex environments. These improve previously known results, bothin terms of theoretical guarantees and in simulations. In addition, we disprovean existing claim in the literature on a lower bound for a solution to thesample placement problem.

Approximation Algorithms for Robot Tours in Random Fields with Guaranteed Estimation Accuracy