Faster algorithms for finding lowest common ancestors in directed acyclic graphs

We present two new methods for finding a lowest common ancestor (LCA) for each pair of vertices of a directed acyclic graph (dag) on n vertices and m edges. The first method is surprisingly natural and solves the all-pairs LCA problem for the input dag on n vertices and m edges in time O(nm). The second method relies on a novel reduction of the all-pairs LCA problem to the problem of finding maximum witnesses for Boolean matrix product. We solve the latter problem and hence also the all-pairs LCA problem in time O(n2+), where satisfies the equation (1, , 1) = 1 + 2 and (1, , 1) is the exponent of the multiplication of an n

• Type: Journal
• Year: 2006
• Where: ECCC
• Authors: Artur Czumaj, Miroslaw Kowaluk, Andrzej Lingas
• Keywords: All-pairs Lca Problem, Directed Acyclic Graph, ECCC 2006, Lowest Common Ancestor