  We consider the celebrated bound introduced by Conforti and Cornu\'ejols
(1984) for greedy schemes in submodular optimization. The bound assumes a
submodular function defined on a collection of sets forming a matroid and is
based on greedy curvature. We show that the bound holds for a very general
class of string problems that includes maximizing submodular functions over set
matroids as a special case. We also derive a bound that is computable in the
sense that they depend only on quantities along the greedy trajectory. We prove
that our bound is superior to the greedy curvature bound of Conforti and
Cornu\'ejols. In addition, our bound holds under a condition that is weaker
than submodularity.
