A Tree Distance Function Based on Multi-sets

Authors:
Arnoldo José Müller-Molina;Kouichi Hirata;Takeshi Shinohara
Affiliations:
Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan 820-8502;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan 820-8502;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan 820-8502
Venue:
New Frontiers in Applied Data Mining
Year:
2009

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Abstract

We introduce a tree distance function based on multi-sets. We show that this function is a metric on tree spaces, and we design an algorithm to compute the distance between trees of size at most n in O (n 2) time and O (n ) space. Contrary to other tree distance functions that require expensive memory allocations to maintain dynamic programming tables of forests, our function can be implemented over simple and static structures. Additionally, we present a case study in which we compare our function with other two distance functions.