LCA Queries in Directed Acyclic Graphs

  title={LCA Queries in Directed Acyclic Graphs},
  author={Miroslaw Kowaluk and Andrzej Lingas},
We present two 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). As a corollary, we obtain an O(n)-time algorithm for finding genealogical distances considerably improving the previously known O(n) timebound for this problem. The second method relies on a novel reduction of… CONTINUE READING

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