  Finding diverse solutions to optimization problems has been of practical
interest for several decades, and recently enjoyed increasing attention in
research. While submodular optimization has been rigorously studied in many
fields, its diverse solutions extension has not. In this study, we consider the
most basic variants of submodular optimization, and propose two simple greedy
algorithms, which are known to be effective at maximizing monotone submodular
functions. These are equipped with parameters that control the trade-off
between objective and diversity. Our theoretical contribution shows their
approximation guarantees in both objective value and diversity, as functions of
their respective parameters. Our experimental investigation with maximum vertex
coverage instances demonstrates their empirical differences in terms of
objective-diversity trade-offs.
