Breaking the Sorting Barrier in Shortest Paths

27/08/2025 11 min

Listen "Breaking the Sorting Barrier in Shortest Paths"

Episode Synopsis

This episode presents a deterministic algorithm for the single-source shortest path (SSSP) problem on directed graphs with non-negative edge weights, operating within the comparison-addition model. The core contribution is achieving an O(m log^(2/3) n) time complexity, which is the first to surpass Dijkstra's algorithm's O(m + n log n) bound on sparse graphs, demonstrating that Dijkstra's is not optimal for SSSP.