寻找中介性和四方兼容性的多种解决方案的复杂性
The Complexity of Finding Multiple Solutions to Betweenness and Quartet Compatibility
摘要：
我们发现，在计算生物学中有应用的两个重要问题是ASP完全的，这意味着，给定一个问题的解决方案，它是NP完全的，以决定是否存在另一个解决方案。我们首先表明，变化的介数，这是辐射混合映射相关的问题的根本问题，是ASP完全的。随后，我们使用该结果表明，四方兼容性，一个基本的问题，在遗传学，问一组四位数是否可以表示的父树，也是ASP完成。后一个结果表明，Steel的\sc Quartet Challenge（询问Quartet兼容性的解决方案是否唯一）是coNP完全的。
英文摘要：
We show that two important problems that have applications in computational biology are ASP-complete, which implies that, given a solution to a problem, it is NP-complete to decide if another solution exists. We show first that a variation of Betweenness, which is the underlying problem of questions related to radiation hybrid mapping, is ASP-complete. Subsequently, we use that result to show that Quartet Compatibility, a fundamental problem in phylogenetics that asks whether a set of quartets can be represented by a parent tree, is also ASP-complete. The latter result shows that Steel's \sc Quartet Challenge, which asks whether a solution to Quartet Compatibility is unique, is coNP-complete.
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