Abstract
Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence the genetic variation present in a population. Being able to align sequencing reads to such graphs is a key step for many analyses and its applications include genome assembly, read error correction, and variant calling with respect to a variation graph. Given the wide range of applications of this basic problem, it is surprising that algorithms with optimal runtime are, to the best of our knowledge, yet unknown. In particular, aligning sequences to cyclic graphs currently represents a challenge both in theory and practice. Here, we introduce an algorithm to compute the minimum edit distance of a sequence of length m to any path in a node-labeled directed graph (V, E) in O(|V |+m|E|) time and O(|V |) space. The corresponding alignment can be obtained in the same runtime using 
space. The time complexity depends only on the length of the sequence and the size of the graph. In particular, it does not depend on the cyclicity of the graph, or any other topological features.
