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 based bound proposed by Conforti and Cornu\'ejols. Our bound is also more computationally feasible than most previously proposed curvature based bounds. Finally, we demonstrate the strength of our result on a discrete version sensor coverage problem.

翻译：我们研究在字符串拟阵上选择有限长度字符串以最大化字符串子模函数的优化问题，该类问题比集合拟阵上最大化集合子模函数的问题更为广泛。针对该问题，我们给出了贪婪算法性能的一个下界，并证明该下界优于Conforti和Cornuéjols提出的基于贪婪曲率的边界。我们的边界在计算可行性上也优于以往大多数基于曲率的边界。最后，我们通过离散版本的传感器覆盖问题展示了该结论的优越性。