Computing connected components in an undirected graph is one of the most basic graph problems. Given a graph with n vertices and m edges, you can find its components in linear time O(n + m) using depth-first or breadth-first search. But what if you need to go faster? In this blog post, I will describe a cool new concurrent algorithm for this problem, which I learned this week at the Heidelberg Laureate Forum from Robert Tarjan himself. The algorithm distributes the work among n + m tiny processors that work concurrently most of the time and requires O(log n) global synchronisation rounds. The algorithm is remarkably simple but it’s far from obvious that it works correctly and efficiently. Happily, Tarjan and his co-author S. Cliff Liu have done all the hard proofs in their recent paper, so we can simply take the algorithm and use it.