## Computing the edit-distance between unrooted ordered trees (1998)

Venue: | In Proceedings of the 6th annual European Symposium on Algorithms (ESA |

Citations: | 81 - 0 self |

### BibTeX

@INPROCEEDINGS{Klein98computingthe,

author = {Philip N. Klein},

title = {Computing the edit-distance between unrooted ordered trees},

booktitle = {In Proceedings of the 6th annual European Symposium on Algorithms (ESA},

year = {1998},

pages = {91--102}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. An ordered tree is a tree in which each node’s incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. WegiveanO(n 3 log n) algorithm to compute the edit distance between two ordered trees. 1

### Citations

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Citation Context ...f Figure 1 gives an example. In stating the time bounds for algorithms, we assume that the cost subroutines take constant time. A more familiar edit-distance problem is computing string edit-distance =-=[7-=-]. The edit-distance between two strings is the minimum cost of a set of symboldeletions and symbol-modications required to turn them into the same string. ? research supported by NSF Grant CCR-970014... |

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Citation Context ...if each node is assigned a cyclic ordering of its incident edges. Such an assignment of cyclic orderings constituted a combinatorial planar embedding of the tree (and is called a rotation system; see =-=[1-=-]). Several application areas involve the comparison between planar embedded trees. Two examples are biochemistry (comparing the secondary structures of dierent RNA molecules) and computer vision (com... |

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Citation Context ...s of T 0 with respect to P (T 0 ). Lemma 3. The number of relevant substrings of T is at most 2jT j log jT j Proof. The proof consists in combining a slight modication of Lemma 7 of Zhang and Shasha [=-=10]-=- with our Lemma 2. The analogue of Zhang and Shasha's lemma states that X special subtree T 0 jT 0 j = X v2T collapsed depth of v (1) To prove this equality, note that for each node v, the number of s... |

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Citation Context ...ing in ti. 4.2 Decomposition of a rooted tree into paths The next idea is the employment of a tree decomposition into heavy paths. This decomposition is used, e.g., in the dynamic-tree data structure =-=[4]-=-. Given a rooted tree T , define the weight of each node v of T be the size of the subtree rooted at v. For each nonleaf node v, let heavy(v) denote the child of v having greatest weight (breaking tie... |

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Citation Context ...ee to an edge in the other). In this subsection, we give a recurrence relation for the edit distance dist(s; t) between two substrings. This recurrence relation implies a dynamic program|in 1 Shapiro =-=[3]-=- compares trees by comparing their Euler strings. However, he does not seem to treat paired darts in any special way; he compares the strings using an ordinary string-edit distance algorithm. Thus he ... |

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On the editing distance between unordered labeled trees
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Citation Context ...omparison of unordered trees would make more sense. Unfortunately, computing edit-distance on unordered trees is NP-complete, as shown by Zhang, Statman, and Shasha [12]. Zhang has given an algorithm =-=[9]-=- for computing a kind of constrained edit-distance between unordered trees. One might consider generalizing from edit-distance between ordered trees to edit-distance between planar graphs. However, th... |

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Citation Context ...n ordinary edit-distance. This brute-force approach reduces a cyclic edit-distance instance to n ordinary edit-distance instances, and hence yields an O(n 3 )-time algorithm. An algorithm due to Maes =-=[2]-=- takes O(n 2 log n) time. The problem of rooted ordered tree edit-distance has previously been considered. This problem arises in settings where, e.g., parse trees need to be compared, such as in natu... |

17 |
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Citation Context ...g in t i . 4.2 Decomposition of a rooted tree into paths The next idea is the employment of a tree decomposition into heavy paths. This decomposition is used, e.g., in the dynamic-tree data structure =-=[4-=-]. Given a rooted tree T , dene the weight of each node v of T be the size of the subtree rooted at v. For each nonleaf node v, let heavy(v) denote the child of v having greatest weight (breaking ties... |

2 | Approximate Tree Pattern Matching, chapter 14 Pattern Matching Algorithms - Shasha, Zhang - 1997 |