从对称到非对称：参数化推广TSP近似
From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization
摘要：
我们推广的树加倍和Christofides算法，两个最常见的近似TSP，参数化近似ATSP。我们考虑的参数为各自的参数化的上限的数量在给定的情况下，不对称的距离，从而产生算法，以有效地计算常数因子近似也适度不对称TSP的情况。作为Christofides算法的推广，我们得到了一个参数化的2.5-近似，其中参数是由非对称边诱导的子图的顶点覆盖的大小。我们的推广的树加倍算法给出了一个参数化的3-近似，其中的参数是在一个给定的最小生成树形图的非对称边的数量。这两种算法也表示在加性有损核化的形式，这允许将它们与已知的多项式时间近似ATSP。此外，我们将它们与对称松弛的概念相结合，允许交易近似保证运行时。我们补充我们的结果的实验评估，这表明，广义树加倍经常优于广义Christofides参数大小。
英文摘要：
We generalize the tree doubling and Christofides algorithm, the two most common approximations for TSP, to parameterized approximations for ATSP. The parameters we consider for the respective parameterizations are upper bounded by the number of asymmetric distances in the given instance, which yields algorithms to efficiently compute constant factor approximations also for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, where the parameter is the size of a vertex cover for the subgraph induced by the asymmetric edges. Our generalization of the tree doubling algorithm gives a parameterized 3-approximation, where the parameter is the number of asymmetric edges in a given minimum spanning arborescence. Both algorithms are also stated in the form of additive lossy kernelizations, which allows to combine them with known polynomial time approximations for ATSP. Further, we combine them with a notion of symmetry relaxation which allows to trade approximation guarantee for runtime. We complement our results by experimental evaluations, which show that generalized tree-doubling frequently outperforms generalized Christofides with respect to parameter size.
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