WGT: Tools and algorithms for recognizing, visualizing, and generating Wheeler graphs

A Wheeler graph represents a collection of strings in a way that is particularly easy to index and query. Such a graph is a practical choice for representing a graph-shaped pangenome, and it is the foundation for current graph-based pangenome indexes. However, there are no practical tools to visualize or to check graphs that may have the Wheeler properties. Here, we present Wheelie, an algorithm that combines a renaming heuristic with a permutation solver (Wheelie-PR) or a Satisfiability Modulo Theory (SMT) solver (Wheelie-SMT) to check whether a given graph has the Wheeler properties, a problem that is NP-complete in general. Wheelie can check a variety of random and real-world graphs in far less time than any algorithm proposed to date. It can check a graph with 1,000s of nodes in seconds. We implement these algorithms together with complementary visualization tools in the WGT toolkit, available as open source software at https://github.com/Kuanhao-Chao/Wheeler_Graph_Toolkit.