We obtain a polynomial-time deterministic $(\frac{2e}{e-1}+ϵ)$-approximation algorithm for maximizing symmetric submodular functions under a budget constraint. Although there exist randomized algorithms with better expected performance, our algorithm achieves the best known factor achieved by a deterministic algorithm, improving on the previously known factor of 6. Furthermore, it is simple, combining two elegant algorithms for related problems; the local search algorithm of Feige, Mirrokni and Vondrák [1] for unconstrained submodular maximization, and the greedy algorithm of Sviridenko [2] for non-decreasing submodular maximization subject to a knapsack constraint.

我们获得多项式时间确定性 $（\frac{2Ë}{Ë-\mathrm{1个}}+ϵ）$-近似算法用于在预算约束下最大化对称子模函数。尽管存在具有更好预期性能的随机算法，但我们的算法在确定性算法的基础上实现了已知因子的最佳已知因子，改进了先前已知的因子6。Feige，Mirrokni和Vondrák[1]的局部搜索算法用于无约束子模最大化，而Sviridenko [2]的贪婪算法用于具有背包约束的非递减子模最大化。