What question did this study set out to answer?

This research aims to connect deterministic graph theory with robust optimization through interval arithmetic.

April 12, 2026Open Access

Robust Interval Estimation in Shortest Path Algorithms via Johnson's Reweighting

Key Points

This research aims to connect deterministic graph theory with robust optimization through interval arithmetic.
Applied interval arithmetic principles to Johnson's reweighting algorithm for sparse graphs
Incorporated the Bellman-Ford invariant to manage negative edge weights
Defined deterministic robust intervals and verified theorems using Lean 4
Shortest path optimality is preserved under bounded uncertainty
Robust intervals are defined mathematically and verified
The integration of interval arithmetic enhances the reliability of the algorithm

Abstract

We introduce a formalized mathematical bridge between deterministic graph theory and robust optimization. By applying principlesof interval arithmetic to Johnson’s reweighting algorithm for sparsegraphs, we demonstrate that shortest path optimality is strictly preserved under bounded uncertainty. Natively incorporating the BellmanFord invariant to handle negative edge weights, we explicitly define deterministic robust intervals. The theorems have been machine-verifiedin Lean 4

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