所有排列超序列为coNP-complete
All Permutations Supersequence is coNP-complete
摘要：
我们证明了，决定一个给定的输入字是否包含作为子序列的整数$\{1,2,\ldots,n\}$的每一个可能的置换是coNP-完全的。即使在给定输入字包含相同整数集上的所有长度为$n-1$的序列作为连续性的保证时，coNP完全性也成立。我们还显示NP-完全性的相关问题的部分非交叉完美匹配的二分图，即找到一个完美的匹配在有序的二分图中的边的匹配事件到选定的顶点（甚至只有从一侧）是非交叉的。
英文摘要：
We prove that deciding whether a given input word contains as subsequence every possible permutation of integers $\{1,2,\ldots,n\}$ is coNP-complete. The coNP-completeness holds even when given the guarantee that the input word contains as subsequences all of length $n-1$ sequences over the same set of integers. We also show NP-completeness of a related problem of Partially Non-crossing Perfect Matching in Bipartite Graphs, i.e. to find a perfect matching in an ordered bipartite graph where edges of the matching incident to selected vertices (even only from one side) are non-crossing.
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