The level-ancestor problem on pure pointer machines

Authors:
Desh Ranjan;Enrico Pontelli
Affiliations:
Department of Computer Science, New Mexico State University, Las Cruces, NM;Department of Computer Science, New Mexico State University, Las Cruces, NM
Venue:
Information Processing Letters
Year:
2003

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Abstract

For a tree T the Level-Ancestor problem is the following: given a node x and an integer depth d, find the ancestor of x in T that is at depth d in T. We formulate this problem precisely for the Pure Pointer Machine model, i.e., pointer machines without arithmetic capabilities. We then provide a solution for the problem in the fully dynamic case that runs in worst-case O(lgn) time per operation. We also prove a matching lower bound of Ω (lg n) to solve the problem.