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Compromise or optimize? The breakpoint anti-median

机译：妥协或优化？ 断点反中位数

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The median of k ≥ 3 genomes was originally defined to find a compromise genome indicative of a common ancestor. However, in gene order comparisons, the usual definitions based on minimizing the sum of distances to the input genomes lead to degenerate medians reflecting only one of the input genomes. "Near-medians", consisting of equal samples of gene adjacencies from all the input genomes, were designed to restore the idea of compromise to the median problem. We explore adjacency sampling constructions in full generality in the case k = 3, with given overlapping sets of adjacencies in the three genomes, where all adjacencies in two-way or three-way overlaps are included in the sample. We require the construction to be maximal, in the sense that no additional proportion of adjacencies from any of genomes may be added without violating the local linearity of the genome. We discover that in incorporating as many adjacencies as possible, evenly from all the input genomes, we are actually maximizing, rather than minimizing, the sum of distances over all other maximal sampling schemes. We propose to explore compromise instead of parsimony as the organizing principle for the small phylogeny problem.
机译：最初定义了K≥3基因组的中位数，以找到指示普通祖先的折衷基因组。然而，在基因令比较中，基于最小化对输入基因组的距离之和的通常定义导致反映其中一个输入基因组的退化中位数。由来自所有输入基因组的基因邻接的相同样本组成的“近代”，旨在恢复对中位问题的妥协的想法。我们在k = 3中探讨全部一般性的邻接采样结构，其中三个基因组中的给定重叠的邻接集合，其中双向或三通重叠的所有邻接都包括在样品中。我们需要建筑物是最大的，因此可以在不违反基因组的局部线性的情况下添加来自任何基因组的额外邻接的额外邻近的邻接。我们发现，在尽可能多的邻接中，均匀地从所有输入基因组纳入其中，我们实际上最大化，而不是最小化，而不是最小化所有其他最大采样方案的距离之和。我们建议探索妥协而不是关于小学发育问题的组织原则。

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