The Serial Transitive Closure Problem for Trees

The serial transitive closure problem is the problem of, given a directed graph G and a list of edges, called closure edges, which are in the transitive closure of the graph, to generate all the closure edges from edges in G . We give a nearly linear upper bound on the number of steps in optimal solutions to the serial transitive closure problem for the case of graphs which are trees. “Nearly linear” means O(n · α(n)) where α is the inverse Ackermann function. This upper bound is optimal to within a constant factor.