  We provide theoretical bounds on the worst case performance of the greedy
algorithm in seeking to maximize a normalized, monotone, but not necessarily
submodular objective function under a simple partition matroid constraint. We
also provide worst case bounds on the performance of the greedy algorithm in
the case that limited information is available at each planning step. We
specifically consider limited information as a result of unreliable
communications during distributed execution of the greedy algorithm. We utilize
notions of curvature for normalized, monotone set functions to develop the
bounds provided in this work. To demonstrate the value of the bounds provided
in this work, we analyze a variant of the benefit of search objective function
and show, using real-world data collected by an autonomous underwater vehicle,
that theoretical approximation guarantees are achieved despite
non-submodularity of the objective function.
