Bipartite matching is in NC!

Since I’m a good mood today—at a beautiful science camp with my kids, high in the mountains near Big Bear Lake in California—I thought I’d blog about something positive. Last week, five authors posted a major paper to the Electronic Colloquium on Computational Complexity, which shows (or anyway, credibly claims to show) that the Bipartite Matching problem is in the complexity class NC. Assuming this stands, it resolves a central problem in parallel algorithms and derandomization that’s been open...