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.

翻译：我们考虑 Conforti 和 Cornuéjols（1984）提出的关于子模优化中贪心策略的著名界。该界假设定义在构成拟阵的集合族上的子模函数，并基于贪心曲率。我们证明该界适用于一类非常广泛的字符串问题，这类问题包括在集合拟阵上最大化子模函数作为特例。我们还推导出一个可计算的界，即该界仅依赖于贪心轨迹上的量。我们证明我们的界优于 Conforti 和 Cornuéjols 的贪心曲率界。此外，我们的界在比子模性更弱的条件下成立。