NDLI: Simple Fast Algorithms for the Editing Distance between Trees and Related Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Zhang, Kaizhong Shasha, Dennis
Copyright Year	1989
Abstract	Ordered labeled trees are trees in which the left-to-right order among siblings is significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree matching is also considered. Specifically, algorithms are designed to answer the following kinds of questions:1. What is the distance between two trees? 2. What is the minimum distance between $T_1 $ and $T_2 $ when zero or more subtrees can be removed from $T_2 $? 3. Let the pruning of a tree at node n mean removing all the descendants of node n. The analogous question for prunings as for subtrees is answered.A dynamic programming algorithm is presented to solve the three questions in sequential time $O(\|T_1 \| \times \|T_2 \| \times \min ({\textit{depth}}(T_1 ),{\textit{leaves}}(T_1 )) \times \min ({\textit{depth}}(T_2 ),{\textit{leaves}}(T_2 )))$ and space $O(\|T_1 \| \times \|T_2 \|)$ compared with $O(\|T_1 \| \times \|T_2 \| \times ({\textit{depth}}(T_1 ))^2 \times ({\textit{depth}}(T_2 ))^2 )$ for the best previous published algorithm due to Tai [J. Assoc. Comput. Mach., 26 (1979), pp, 422-433]. Further, the algorithm presented here can be parallelized to give time $O(\|T_1 \| \times \|T_2 \|)$.
Starting Page	1245
Ending Page	1262
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/0218082
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	18
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	Analysis of algorithms and problem complexity parallel algorithm dynamic programming Data structures Graph theory editing distance trees pattern recognition
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in