The Complexity of Regular Trail and Simple Path Queries on Undirected Graphs

We study the data complexity of regular trail and simple path queries on undirected graphs. Using techniques from structural graph theory, ranging from the graph minor theorem to group-labeled graphs, we are able to identify several tractable and intractable subclasses of the regular languages. In particular, we establish that trail evaluation for simple chain regular expressions, which are common in practice, is tractable, whereas simple path evaluation is tractable for a large subclass. The problem of fully classifying all regular languages is quite non-trivial, even on undirected graphs, since it subsumes an intriguing problem that has been open for 30 years.