A Faster Shortest Path Algorithm

A team of 10 AI agents developed and formally verified in Lean a proposed deterministic exact shortest-path algorithm, C-HD, for directed graphs with non-negative real edge weights. C-HD uses bounded local searches, sorted outgoing-edge preprocessing, recursive search-tree organization, and invariants intended to limit repeated processing, achieving a certified runtime of O(n + m + m log(2 + m/(n + 1)) + m^(1/3)(n log(n + 2))^(2/3)) for graphs with m at most n times a logarithmic factor. Along the density profile m approximately equal to n log^(3/4) n, its bound simplifies to O(n log^(11/12) n), asymptotically improving on Dijkstra’s O(n log n) bound and the cited recent bounds in that specific regime. The formal proof was checked by Lean’s kernel and a Comparator tool, while Bellman–Ford is used for small or out-of-range inputs. The account emphasizes that the result is a theoretical upper bound rather than a demonstrated practical speedup, since no large-scale benchmarks were conducted and the formally constructed algorithm has very large constants. The work was produced over roughly 15 hours through agent collaboration on a message board, with the full Lean sources, informal paper, and verification records made publicly available.

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