We study the optimization problem of choosing strings of finite length to maximize string submodular functions on string matroids, which is a broader class of problems than maximizing set submodular functions on set matroids. We provide a lower bound for the performance of the greedy algorithm in our problem, and then prove that our bound is superior to the greedy curvature bound of Conforti and Cornuejols. Our bound has lower computational complexity than most previously proposed curvature bounds. Finally, we demonstrate the strength of our result on a sensor coverage problem.

翻译：我们研究在弦拟阵上选择有限长度弦以最大化弦子模函数的优化问题，这是比在集合拟阵上最大化集合子模函数更广泛的一类问题。我们给出了该问题中贪婪算法性能的下界，并证明该下界优于Conforti和Cornuejols提出的贪婪曲率界。我们的下界比大多数先前提出的曲率界具有更低的计算复杂度。最后，我们在传感器覆盖问题上展示了所提结果的有效性。