在图中寻找极大精确匹配
Finding Maximal Exact Matches in Graphs
AI总结：
本文研究在查询字符串与标记图间寻找极大精确匹配（MEMs）的问题，提出一种多项式时间复杂度算法寻找特定长度的$κ$-MEMs，并在可索引的Elastic Founder Graphs上开发了高效的解决方案，实验证明图MEMs数量显著少于字符串MEMs。
摘要：
我们研究在查询字符串$Q$与标记图$G$之间寻找极大精确匹配（MEMs）的问题。MEMs是一类重要的种子，由于与经典度量有紧密联系，常用于seed-chain-extend类型的实用比对方法中。加速chaining的一种有原则的方法是仅考虑长度至少为$κ$的MEMs（$κ$-MEMs）来限制MEMs的数量。然而，在任意输入图上，在SETH下，寻找MEMs的问题无法在真正的亚二次时间内解决（Equi等人，ICALP 2019），即使是在无环图上也是如此。在本文中，我们提出了一种时间复杂度为$O(n\cdot L \cdot d^{L-1} + m + M_{κ,L})$的算法，用于寻找$Q$与$G$之间在$G$中恰好跨越$L$个节点的所有$κ$-MEMs，其中$n$是节点标签的总长度，$d$是$G$中节点的最大度数，$m = |Q|$，$M_{κ,L}$是输出的MEMs数量。我们利用该算法在可索引的Elastic Founder Graphs（Equi等人，Algorithmica 2022）上开发了一种$κ$-MEM寻找解决方案，运行时间为$O(nH^2 + m + M_κ)$，其中$H$是一个块中的最大节点数，$M_κ$是$κ$-MEMs的总数。我们的结果可推广至多个查询字符串的分析（$G$与任意字符串之间的MEMs）。此外，我们提供了一些初步实验结果，表明图MEMs的数量比相应拼接集合的字符串MEMs数量小一个数量级。
英文摘要：
We study the problem of finding maximal exact matches (MEMs) between a query string $Q$ and a labeled graph $G$. MEMs are an important class of seeds, often used in seed-chain-extend type of practical alignment methods because of their strong connections to classical metrics. A principled way to speed up chaining is to limit the number of MEMs by considering only MEMs of length at least $κ$ ($κ$-MEMs). However, on arbitrary input graphs, the problem of finding MEMs cannot be solved in truly sub-quadratic time under SETH (Equi et al., ICALP 2019) even on acyclic graphs. In this paper we show an $O(n\cdot L \cdot d^{L-1} + m + M_{κ,L})$-time algorithm finding all $κ$-MEMs between $Q$ and $G$ spanning exactly $L$ nodes in $G$, where $n$ is the total length of node labels, $d$ is the maximum degree of a node in $G$, $m = |Q|$, and $M_{κ,L}$ is the number of output MEMs. We use this algorithm to develop a $κ$-MEM finding solution on indexable Elastic Founder Graphs (Equi et al., Algorithmica 2022) running in time $O(nH^2 + m + M_κ)$, where $H$ is the maximum number of nodes in a block, and $M_κ$ is the total number of $κ$-MEMs. Our results generalize to the analysis of multiple query strings (MEMs between $G$ and any of the strings). Additionally, we provide some preliminary experimental results showing that the number of graph MEMs is an order of magnitude smaller than the number of string MEMs of the corresponding concatenated collection.
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。
