An Algorithm for Finding the Largest Approximately Common Substructures of Two Trees

  • Authors:

  • Jason T. L. Wang;Bruce A. Shapiro;Dennis Shasha;Kaizhong Zhang;Kathleen M. Currey

  • Affiliations:

  • New Jersey Institute of Technology, Newark;National Cancer Institute, Frederick, MD;New York Univ., New York, NY;Univ. of Western Ontario, London, Ont., Canada;National Cancer Institute, Frederick, MD/ and Univ. of Maryland Medical Center, Baltimore

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1998

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Abstract

Ordered, labeled trees are trees in which each node has a label and the left-to-right order of its children (if it has any) is fixed. Such trees have many applications in vision, pattern recognition, molecular biology and natural language processing. We consider a substructure of an ordered labeled tree T to be a connected subgraph of T. Given two ordered labeled trees T1 and T2 and an integer d, the largest approximately common substructure problem is to find a substructure U1 of T1 and a substructure U2 of T2 such that U1 is within edit distance d of U2 and where there does not exist any other substructure V1 of T1 and V2 of T2 such that V1 and V2 satisfy the distance constraint and the sum of the sizes of V1 and V2 is greater than the sum of the sizes of U1 and U2. We present a dynamic programming algorithm to solve this problem, which runs as fast as the fastest known algorithm for computing the edit distance of two trees when the distance allowed in the common substructures is a constant independent of the input trees. To demonstrate the utility of our algorithm, we discuss its application to discovering motifs in multiple RNA secondary structures (which are ordered labeled trees).