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

Koo, Jaehyun

doi:10.4230/LIPIcs.FUN.2024.19

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Document Identifiers

DOI: 10.4230/LIPIcs.FUN.2024.19
URN: urn:nbn:de:0030-drops-199270

Author Details

Jaehyun Koo

MIT EECS and CSAIL, Cambridge, MA, USA

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Jaehyun Koo. Anarchy in the APSP: Algorithm and Hardness for Incorrect Implementation of Floyd-Warshall. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 19:1-19:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FUN.2024.19

Abstract

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.

Subject Classification

ACM Subject Classification

Theory of computation → Shortest paths
Theory of computation → Problems, reductions and completeness

Keywords

fine-grained complexity
recreational algorithms

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References

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