A math problem that’s been stumped for 43 years finally got solved, and this time, there’s zero room for argument.
April 3, 2026
Original Paper
Bipartite Exact Matching in P
arXiv · 2604.01571
AI-generated illustration
The Takeaway
Computer scientists have relied on 'luck' and randomness to solve this problem since the 80s, but could never prove it was always possible. This breakthrough closes a major gap in our understanding of what computers can do without relying on chance.
From the abstract
The Exact Matching problem asks whether a bipartite graph with edges colored red and blue admits a perfect matching with exactly t red edges. Introduced by Papadimitriou and Yannakakis in 1982, the problem has resisted deterministic polynomial-time algorithms for over four decades, despite admitting a randomized solution via the Schwartz-Zippel lemma since 1987. We prove the Affine-Slice Nonvanishing Conjecture (ASNC) for all bipartite braces and give a deterministic O(n^6) algorithm for Exact M