Subquadratic 3SUM and Subcubic APSP

Researchers report the first polynomial speedups over classic textbook bounds for 3SUM and APSP, including deterministic algorithms that improve 3SUM to O(n^1.9992) and APSP to O(n^2.9995). For CIOs and technology leaders, the strategic takeaway is less about immediate product changes and more about a major shift in computational complexity assumptions: several long-standing hardness conjectures underpinning algorithmic research, optimization methods, and related theoretical limits have been refuted, which can unlock faster graph, matrix, and dependency-analysis workloads over time.