混合多风约束弧路由问题的参数化近似算法：理论与实验
A parameterized approximation algorithm for the mixed and windy Capacitated Arc Routing Problem: theory and experiments
摘要：
我们证明了任何多项式时间$α(n)$ -近似算法的$n$ -顶点度量不对称的旅行商问题产生一个多项式时间$O(α(C))$ -近似算法的混合和风的容量限制弧路由问题，其中$C$是弱连接组件的数量在子图中引起的正需求弧-在许多应用中的一个小数目。结合已知的结果，我们得到的常数因子近似的$C\in O(\log n)$和$O(\log C/\log\log C)$ -近似一般。实验表明，我们的算法，连同一些启发式增强，优于许多以前的多项式时间的启发式。最后，由于在多项式时间内实现的解决方案的质量似乎主要取决于$C$，因为$C=1$在几乎所有的基准实例，我们提出了Ob基准集，模拟城市分为几个组成部分的河流。
英文摘要：
We prove that any polynomial-time $α(n)$-approximation algorithm for the $n$-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time $O(α(C))$-approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where $C$ is the number of weakly connected components in the subgraph induced by the positive-demand arcs---a small number in many applications. In conjunction with known results, we obtain constant-factor approximations for $C\in O(\log n)$ and $O(\log C/\log\log C)$-approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial-time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on $C$ and since $C=1$ in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river.
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