Verifying Shortest Paths in Linear Time

TL;DR

The paper tackles verifiable correctness for the single-source shortest-path problem in graphs with mixed arc weights. It introduces a linear-time certifying algorithm where a prover supplies distances $D[v]$ and a verifier checks four constraints to confirm $D[v] = d[v]$ without recomputing shortest paths. The key contributions are extending certifying verification to graphs with negative and zero weights, proving correctness through feasibility arguments, and achieving an overall $O(n+m)$ verification time. This approach enables fast, reliable validation and benchmarking of shortest-path results in practical applications, reducing the need for expensive recomputation with algorithms like Bellman-Ford.

Abstract

In this paper we propose a linear-time certifying algorithm for the single-source shortest-path problem capable of verifying graphs with positive, negative, and zero arc weights. Previously proposed linear-time approaches only work for graphs with positive arc weights.