Anarchy in the APSP: Algorithm and Hardness for Incorrect Implementation of Floyd-Warshall

The celebrated Floyd-Warshall algorithm efficiently computes the all-pairs shortest path, and its simplicity made it a staple in computer science classes. Frequently, students discover a variant of this Floyd-Warshall algorithm by mixing up the loop order, ending up with the incorrect APSP matrix. This paper considers a computational problem of computing this incorrect APSP matrix. We will propose efficient algorithms for this problem and prove that this incorrect variant is APSP-complete.