SIAM Journal on Matrix Analysis and Applications, Volume 42, Issue 3, Page 1337-1364, January 2021.
In 2017 Pichon et al. introduced an effective method for reordering columns within supernodes based on reformulating the underlying optimization problem as a set of traveling salesman problems (TSPs), one for each supernode. The primary problem with their approach is its cost in time, and the primary bottleneck is computing the TSP distances. We introduce techniques that dramatically reduce the time required by their method. First, we introduce a straightforward technique for reducing the size of a TSP, thereby reducing the number of TSP distances that must be computed and also reducing the cost of computing the TSP tour afterward. Second, we introduce a more complex and efficient algorithm for computing the TSP distances that exploits the fact that the relevant sets induce subtrees in the supernodal elimination tree.

中文翻译：

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在超级节点内重新排序列的旅行商问题方法的快速实现

SIAM Journal on Matrix Analysis and Applications，第 42 卷，第 3 期，第 1337-1364 页，2021 年 1 月。
2017 年，Pichon 等人。基于将底层优化问题重新表述为一组旅行商问题 (TSP)，每个超级节点一个，引入了一种重新排序超级节点内列的有效方法。他们的方法的主要问题是时间成本，主要瓶颈是计算 TSP 距离。我们介绍的技术可以大大减少他们的方法所需的时间。首先，我们引入了一种减少 TSP 大小的直接技术，从而减少了必须计算的 TSP 距离的数量，并降低了之后计算 TSP 旅行的成本。其次，我们引入了一种更复杂、更有效的算法来计算 TSP 距离，该算法利用了相关集在超节点消除树中诱导子树的事实。