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A Metric Between Unrooted and Unordered Trees and its Bottom-Up Computing Method
December 1994 (vol. 16 no. 12)
pp. 1233-1238

Proposes a distance measure between unrooted and unordered trees based on the strongly structure-preserving mapping (SSPM). SSPM can make correspondences between the vertices of similar substructures of given structures more strictly than previously proposed mappings. The time complexity of computing the distance between trees T/sub a/ and T/sub b/ is O(m/sub bsup 3/N/sub a/N/sub b/), where N/sub a/ and N/sub b/ are the number of vertices in trees T/sub a/ and T/sub b/, respectively; m/sub a/ and m/sub b/ are the maximum degrees of a vertex in T/sub a/ and T/sub b/, respectively; and m/sub aspl les/m/sub b/ is assumed. The space complexity of the method is O(N/sub a/N/sub b/).

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Index Terms:
trees (mathematics); computational complexity; dynamic programming; pattern matching; distance metric; unrooted trees; unordered trees; bottom-up computing method; strongly structure-preserving mapping; vertex correspondences; similar substructures; time complexity; maximum degrees; space complexity; dynamic programming; pattern matching; pattern recognition; similar structure search; similarity
Citation:
E. Tanaka, "A Metric Between Unrooted and Unordered Trees and its Bottom-Up Computing Method," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 12, pp. 1233-1238, Dec. 1994, doi:10.1109/34.387483
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