In graph theory and theoretical computer science, the level ancestor problem is the problem of preprocessing a given rooted tree T into a data structure that can determine the ancestor of a given node at a given distance from the root of the tree.
More precisely, let T be a rooted tree with n nodes, and let v be an arbitrary node of T. The level ancestor query LA(v,d) requests the ancestor of node v at depth d, where the depth of a node v in a tree is the number of edges on the shortest path from the root of the tree to node v.
It is possible to solve this problem in constant time per query, after a preprocessing algorithm that takes O(n) and that builds a data structure that uses O(n) storage space.[1][2]
^Bender, Michael A.; Farach-Colton, Martin (2004). "The Level Ancestor Problem Simplified". Theor. Comput. Sci. 321: 5–12. doi:10.1016/j.tcs.2003.05.002.
^Berkman, Omer; Vishkin, Uzi (Apr 1994). "Finding level-ancestors in trees". J. Comput. Syst. Sci. 2. 48 (2): 214–230. doi:10.1016/S0022-0000(05)80002-9.
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