An Optimal Algorithm for Finding NCA on Pure Pointer Machines

Authors:
Alessandro Dal Palú;Enrico Pontelli;Desh Ranjan
Affiliations:
-;-;-
Venue:
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Year:
2002

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Abstract

We present a simple, arithmetic-free, efficient scheme to compress trees maintaining the nearest common ancestor (NCA) information. We use this compression scheme to provide an O(n + q lg lg n) solution for solving the NCA problem on Pure Pointer Machines (PPMs) (i.e., pointer machines with no arithmetic capabilities) in both the static and dynamic case, where n is the number of add-leaf/delete operations and q is the number of NCA queries. This solution is optimal.