次模函数近似算法求最小弱顶点覆盖

求给定无向图的最小弱顶点覆盖是一个NP困难问题，只能通过研究此问题的近似算法来求解。本文从基本圈出发，定义了一个次模函数，利用次模函数理论来得到一个最小弱顶点覆盖问题的近似解，且近似度为1+ln(d-1)，其中d为图的顶点最大度。

Submodular potential function for the minimum weak vertex cover problem

The minimum weak vertex cover problem is non-deterministic polynomial-time hard(NP-hard),and thus we can only produce an approximate solution to this problem.Here we start from a fundamental cycle to define a submodular potential function.Then using the theory of submodular potential functions,we give an approximation algorithm to solve the problem.The approximation factor of the algorithm is 1+ ln(d-1),where d is the maximum degree of the vertices.