可索引弹性基础图的线性时间构造
Linear Time Construction of Indexable Elastic Founder Graphs
AI总结：
针对图模式匹配的二次下界瓶颈，本文利用后缀树和树上祖先问题，将多序列比对预处理改进至O(mn)时间，使两类可索引弹性基础图均能在线性时间内构造。
摘要：
图上的模式匹配由于其在基因组学应用中的重要性近来被广泛研究。遗憾的是，即使在正交向量假设下，判断一个字符串是否作为子路径出现在图中这一最简单的问题也存在二次下界。为避免此瓶颈，研究转向更特定的图类，例如由多序列比对诱导的图。考虑将MSA[1..m,1..n]分割为b个块。在移除间隙符号后，块各行中的不同字符串构成弹性基础图（EFG）的节点，边表示MSA中观察到的原始连接。若节点标签仅作为从同一块节点开始的路径的前缀，则EFG称为可索引的。研究表明此类EFG支持快速模式匹配，并给出了O(mn log m)时间的预处理算法，使得可在O(n)和O(n log log n)时间内分别构造最大化块数和最小化块最大长度的可索引EFG。通过使用后缀树并解决树上祖先问题，我们将预处理改进为O(mn)时间，将O(n log log n)时间的EFG构造改进为O(n)时间，从而证明两类可索引EFG均可在输入大小的线性时间内构造。
英文摘要：
Pattern matching on graphs has been widely studied lately due to its importance in genomics applications. Unfortunately, even the simplest problem of deciding if a string appears as a subpath of a graph admits a quadratic lower bound under the Orthogonal Vectors Hypothesis (Equi et al. ICALP 2019, SOFSEM 2021). To avoid this bottleneck, the research has shifted towards more specific graph classes, e.g. those induced from multiple sequence alignments (MSAs). Consider segmenting $\mathsf{MSA}[1..m,1..n]$ into $b$ blocks $\mathsf{MSA}[1..m,1..j_1]$, $\mathsf{MSA}[1..m,j_1+1..j_2]$, $\ldots$, $\mathsf{MSA}[1..m,j_{b-1}+1..n]$. The distinct strings in the rows of the blocks, after the removal of gap symbols, form the nodes of an elastic founder graph (EFG) where the edges represent the original connections observed in the MSA. An EFG is called indexable if a node label occurs as a prefix of only those paths that start from a node of the same block. Equi et al. (ISAAC 2021) showed that such EFGs support fast pattern matching and gave an $O(mn \log m)$-time algorithm for preprocessing the MSA in a way that allows the construction of indexable EFGs maximizing the number of blocks and, alternatively, minimizing the maximum length of a block, in $O(n)$ and $O(n \log\log n)$ time respectively. Using the suffix tree and solving a novel ancestor problem on trees, we improve the preprocessing to $O(mn)$ time and the $O(n \log \log n)$-time EFG construction to $O(n)$ time, thus showing that both types of indexable EFGs can be constructed in time linear in the input size.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
