  We study the sample placement and shortest tour problem for robots tasked
with mapping environmental phenomena modeled as stationary random fields. The
objective is to minimize the resources used (samples or tour length) while
guaranteeing estimation accuracy. We give approximation algorithms for both
problems in convex environments. These improve previously known results, both
in terms of theoretical guarantees and in simulations. In addition, we disprove
an existing claim in the literature on a lower bound for a solution to the
sample placement problem.
