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Polynomial-time metrics for attributed trees.

Andrea Torsello1, Dzena Hidović-Rowe, Marcello Pelillo

  • 1Dipartimento di Informatica, Università Ca' Foscari di Venezia, Via Torino 155, 30172 Venezia Mestre, Italy. torsello@dsi.unive.it

IEEE Transactions on Pattern Analysis and Machine Intelligence
|July 15, 2005
PubMed
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We introduce new ways to compare attributed trees using maximal similarity common subtrees. Our efficient methods are faster than traditional approaches and work for various tree types and attributes.

Area of Science:

  • Computer Science
  • Data Science
  • Graph Theory

Background:

  • Comparing attributed trees is crucial for many applications.
  • Existing methods like edit-distance are often computationally expensive (NP-complete).
  • There is a need for efficient and general tree comparison metrics.

Purpose of the Study:

  • To propose novel distance measures for comparing attributed trees.
  • To develop efficient algorithms for computing these measures.
  • To validate the effectiveness of the proposed measures in practical applications.

Main Methods:

  • Definition of four novel distance measures based on maximal similarity common subtrees.
  • Proof of metric properties for the proposed measures.
  • Development of a polynomial-time algorithm for computing the distances.

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Main Results:

  • The proposed distance measures satisfy metric constraints.
  • A polynomial-time algorithm for computing the measures was developed, offering significant efficiency gains over NP-complete methods.
  • Experimental validation demonstrated the utility of the metrics in shape matching tasks.

Conclusions:

  • The novel distance measures provide an efficient and general approach to comparing attributed trees.
  • The polynomial-time computation makes these measures practical for large-scale applications.
  • The metrics show promise for tasks such as shape matching and data analysis.