Exact and approximate algorithms for unordered tree matching

Dennis Shasha, Jason Tsong Li Wang, Kaizhong Zhang, Frank Y. Shih

Research output: Contribution to journalArticle

Abstract

We consider the problem of comparison between unordered trees, i.e., trees for which the order among siblings is unimportant. The criterion for comparison is the distance as measured by a weighted sum of the costs of deletion, insertion and relabel operations on tree nodes. Such comparisons may contribute to pattern recognition efforts in any field (e.g., genetics) where data can naturally be characterized by unordered trees. In companion work, we have shown this problem to be NP-complete. This paper presents an efficient enumerative algorithm and several heuristics leading to approximate solutions. The algorithms are based on probabilistic hill climbing and bipartite matching techniques. The paper evaluates the accuracy and time efficiency of the heuristics by applying them to a set of trees transformed from industrial parts based on a previously proposed morphological model.

Original languageEnglish (US)
Pages (from-to)668-678
Number of pages11
JournalIEEE Transactions on Systems, Man and Cybernetics
Volume24
Issue number4
DOIs
StatePublished - Apr 1994

Fingerprint

Pattern recognition
Costs
Genetics

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Exact and approximate algorithms for unordered tree matching. / Shasha, Dennis; Wang, Jason Tsong Li; Zhang, Kaizhong; Shih, Frank Y.

In: IEEE Transactions on Systems, Man and Cybernetics, Vol. 24, No. 4, 04.1994, p. 668-678.

Research output: Contribution to journalArticle

Shasha, Dennis ; Wang, Jason Tsong Li ; Zhang, Kaizhong ; Shih, Frank Y. / Exact and approximate algorithms for unordered tree matching. In: IEEE Transactions on Systems, Man and Cybernetics. 1994 ; Vol. 24, No. 4. pp. 668-678.
@article{62bb0996fe82474580a6a7ddad240593,
title = "Exact and approximate algorithms for unordered tree matching",
abstract = "We consider the problem of comparison between unordered trees, i.e., trees for which the order among siblings is unimportant. The criterion for comparison is the distance as measured by a weighted sum of the costs of deletion, insertion and relabel operations on tree nodes. Such comparisons may contribute to pattern recognition efforts in any field (e.g., genetics) where data can naturally be characterized by unordered trees. In companion work, we have shown this problem to be NP-complete. This paper presents an efficient enumerative algorithm and several heuristics leading to approximate solutions. The algorithms are based on probabilistic hill climbing and bipartite matching techniques. The paper evaluates the accuracy and time efficiency of the heuristics by applying them to a set of trees transformed from industrial parts based on a previously proposed morphological model.",
author = "Dennis Shasha and Wang, {Jason Tsong Li} and Kaizhong Zhang and Shih, {Frank Y.}",
year = "1994",
month = "4",
doi = "10.1109/21.286387",
language = "English (US)",
volume = "24",
pages = "668--678",
journal = "IEEE Transactions on Systems, Man and Cybernetics",
issn = "0018-9472",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",

}

TY - JOUR

T1 - Exact and approximate algorithms for unordered tree matching

AU - Shasha, Dennis

AU - Wang, Jason Tsong Li

AU - Zhang, Kaizhong

AU - Shih, Frank Y.

PY - 1994/4

Y1 - 1994/4

N2 - We consider the problem of comparison between unordered trees, i.e., trees for which the order among siblings is unimportant. The criterion for comparison is the distance as measured by a weighted sum of the costs of deletion, insertion and relabel operations on tree nodes. Such comparisons may contribute to pattern recognition efforts in any field (e.g., genetics) where data can naturally be characterized by unordered trees. In companion work, we have shown this problem to be NP-complete. This paper presents an efficient enumerative algorithm and several heuristics leading to approximate solutions. The algorithms are based on probabilistic hill climbing and bipartite matching techniques. The paper evaluates the accuracy and time efficiency of the heuristics by applying them to a set of trees transformed from industrial parts based on a previously proposed morphological model.

AB - We consider the problem of comparison between unordered trees, i.e., trees for which the order among siblings is unimportant. The criterion for comparison is the distance as measured by a weighted sum of the costs of deletion, insertion and relabel operations on tree nodes. Such comparisons may contribute to pattern recognition efforts in any field (e.g., genetics) where data can naturally be characterized by unordered trees. In companion work, we have shown this problem to be NP-complete. This paper presents an efficient enumerative algorithm and several heuristics leading to approximate solutions. The algorithms are based on probabilistic hill climbing and bipartite matching techniques. The paper evaluates the accuracy and time efficiency of the heuristics by applying them to a set of trees transformed from industrial parts based on a previously proposed morphological model.

UR - http://www.scopus.com/inward/record.url?scp=0028406997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028406997&partnerID=8YFLogxK

U2 - 10.1109/21.286387

DO - 10.1109/21.286387

M3 - Article

AN - SCOPUS:0028406997

VL - 24

SP - 668

EP - 678

JO - IEEE Transactions on Systems, Man and Cybernetics

JF - IEEE Transactions on Systems, Man and Cybernetics

SN - 0018-9472

IS - 4

ER -