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A LAYER-DECOMPOSITION WITH DEGREE METHOD FOR SUBGRAPHS RECOGNITION PROBLEM

Yifan Xu
2003 Taiwanese journal of mathematics  
For two planar undirected graphs G and H, the subgraphs recognition problem (SRP) is to find and list all subgraphs of G which are isomorphic to H.  ...  Since subgraphs isomorphic to each other contain their spanning trees with the same decomposition, the SRP can be decomposed into two subproblems: First, find subtrees of G which have the same layerdecomposition  ...  ACKNOWLEDGEMENTS The author wishes to thank anonymous referees for their valuable comments for revision.  ... 
doi:10.11650/twjm/1500407526 fatcat:pdwaqb4n6bes3fmdm2m6ffwova

On the tree packing problem

Shigeru Masuyama
1992 Discrete Applied Mathematics  
., On the tree packing problem, Discrete Applied Mathematics 35 (1992) 163-166.  ...  The maximum tree packing problem asks to pack the greatest possible number of vertex-disjoint trees isomorphic to a fixed tree To, into a given input tree T.  ...  Mine of Kansai University (Professor Emeritus of Kyoto University) for their valuable comments. Thanks are also due to the referee whose comments were greatly beneficial to improve this paper.  ... 
doi:10.1016/0166-218x(92)90040-h fatcat:ycy2jsbd2rghjfo5wnvlapimxe

Faster Subtree Isomorphism

Ron Shamir, Dekel Tsur
1999 Journal of Algorithms  
We study the subtree isomorphism problem: Given trees H and G, find a subtree of G which is isomorphic to H or decide that there is no such subtree.  ...  We also give a randomized (Las Vegas) O(k 1.376 n)-time algorithm for the decision problem. * A preliminary version of this paper has appeared in the Fifth Israel Symposium on Theory of Computing and Systems  ...  Acknowledgment We are grateful to the anonymous referee for a careful reading of the manuscript and many helpful comments.  ... 
doi:10.1006/jagm.1999.1044 fatcat:ldhjebrjmvcrjos2su4c6cocw4

Page 1594 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
on the subtree isomorphism for ordered trees: “On the subtree isomorphism problem for ordered trees” [Inform.  ...  Given two rooted trees P, 7, the subtree isomorphism problem is to decide whether P is isomorphic to a subtree of T.  ... 

Isomorphic Subgraphs [chapter]

Sabine Bachl
1999 Lecture Notes in Computer Science  
We show that the Isomorphic Subgraphs problem is NP-hard for connected outerplanar graphs, and 2-connected planar graphs and is solvable in linear time when restricted to trees.  ...  For a given graph G the Isomorphic Subgraphs problem makes use of the second approach and tries to find the two largest disjoint isomorphic subgraphs in G.  ...  Brandenburg for his various and detailed comments and suggestions, particularly on the proof of Isomorphic Subgraphs of general graphs.  ... 
doi:10.1007/3-540-46648-7_30 fatcat:wiec3yfyk5agpeweik3zz3ybby

Subtree isomorphism is in random NC

Phillip B. Gibbons, Richard M. Karp, Gary L. Miller, Danny Soroker
1990 Discrete Applied Mathematics  
Given two trees, a guest tree G and a host tree H, the subtree isomorphism problem is to determine whether there is a subgraph of H that is isomorphic to G.  ...  We present a randomized parallel algorithm for finding such an isomorphism, if it exists. The algorithm runs in time 0(log3n) on a CREW PRAM, where n is the number of nodes in H.  ...  Let limb-rooted subtree isomorphism be the subtree isomorphism problem restricted to the case where both G and H are limb-rooted trees, i.e., G= L(g) for some edge g in G and H= L(h) for some edge h in  ... 
doi:10.1016/0166-218x(90)90081-m fatcat:aoz3bbcc7fgttecgflfxhydyim

Oblivious Decision Trees, Graphs, and Top-Down Pruning

Ron Kohavi, Chia-Hsin Li
1995 International Joint Conference on Artificial Intelligence  
tin root The pruning mechanism is well suited for finding symmetries and aids in recovering from splits on irrelevant features that mav happen during the tree consLrm tion  ...  nodes at the same level of the tree For domains that art appropriate for both decision trees and OODGs, per formance is approximately the same aS THAT of C45 ), but the number of nodes in the OODG is much  ...  reviewers for comments on the paper We thank Yael Kleefeld and Ya-Huei Wang for their support  ... 
dblp:conf/ijcai/KohaviL95 fatcat:nvs6bezumzdtboeln5dtlg3uoa

Maximum tree-packing in time O(n52)

Andrzej Lingas
1997 Theoretical Computer Science  
The problem of determining the maximum number of node-disjoint subtrees of a tree T on PI, nodes isomorphic to a tree S on nc nodes is shown to be solvable in time O(nj"n,).  ...  The same asymptotic bounds are observed for the corresponding problems where topological imbedding and subgraph homeomorphism are respectively substituted for subgraph isomorphism. *  ...  Acknowledgements Thanks go to Anders Dessmark and an unknown referee for valuable comments.  ... 
doi:10.1016/s0304-3975(96)00276-9 fatcat:7iwcjtax3rbyzhdld4bxwp2rqq

Constrained tree inclusion

Gabriel Valiente
2005 Journal of Discrete Algorithms  
Further, it can be solved in polynomial time for both unordered and ordered trees. Algorithms based on the restricted subtree homeomorphism algorithm of M.-J. Chung [J.  ...  Algorithms 8 (1) (1987) 106-112] are presented that solve the constrained tree inclusion problem in O(m 1.5 n) time on unordered trees with m and n nodes, and in O(mn) time on ordered trees, using O(mn  ...  Acknowledgements The author would like to acknowledge with thanks the anonymous referees, whose comments and criticism have led to a substantial improvement of this paper, and would also like to acknowledge  ... 
doi:10.1016/j.jda.2004.08.017 fatcat:7klol62bkvdz3k74fjgykttjae

Planar Graph Isomorphism is in Log-Space

Samir Datta, Nutan Limaye, Prajakta Nimbhorkar, Thomas Thierauf, Fabian Wagner
2009 2009 24th Annual IEEE Conference on Computational Complexity  
Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity.  ...  The next step is to log-space reduce the biconnected planar graph isomorphism and canonization problems to those for 3-connected planar graphs, which are known to be in log-space by [DLN08].  ...  Arvind, Bireswar Das, Raghav Kulkarni, Meena Mahajan, Jacobo Torán and the anonymous referees for helpful comments and discussions.  ... 
doi:10.1109/ccc.2009.16 dblp:conf/coco/DattaLNTW09 fatcat:kgine7w6tfd6fi4jvylibrw23q

Planar Graph Isomorphism is in Log-Space

Samir Datta, Nutan Limaye, Prajakta Nimbhorkar, Thomas Thierauf, Fabian Wagner
2022 ACM Transactions on Computation Theory  
Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity.  ...  The gap between the known upper and lower bounds continues to be very significant for many subclasses of graphs as well.  ...  Arvind, Bireswar Das, Raghav Kulkarni, Meena Mahajan, Jacobo Torán and the anonymous referees for helpful comments and discussions.  ... 
doi:10.1145/3543686 fatcat:glhtpo6suzgztpmihwy4xew5le

Canonical forms for labelled trees and their applications in frequent subtree mining

Yun Chi, Yirong Yang, Richard R. Muntz
2005 Knowledge and Information Systems  
Then the canonical forms are applied to the frequent subtree mining problem.  ...  Based on the BFCF, we develop a vertical mining algorithm, RootedTreeMiner, to discover all frequently occurring subtrees in a database of labelled rooted unordered trees.  ...  We thank the anonymous reviewers for their very useful comments and suggestions. Thanks to Professor Mohammed J.  ... 
doi:10.1007/s10115-004-0180-7 fatcat:a2qbzzppbbdkdji2duh4lvtb7m

Page 6844 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
{For the entire collection see MR 91m:05005.} 91m:68143 68R10 05C05 68P05 68Q25 Dublish, Pratul (D-HILD-I) Some comments on: “On the subtree isomorphism problem for ordered trees” [Inform. Process.  ...  Introduction: “A linear time algorithm for the subtree isomorphism problem for rooted ordered trees has recently been presented by Makinen in the paper cited in the heading.  ... 

Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics [chapter]

Marcello Pelillo
2001 Lecture Notes in Computer Science  
are in one-to-one correspondence with maximal common subtrees.  ...  Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques  ...  Liu for kindly providing us with the shape database, and the anonymous reviewers for their comments.  ... 
doi:10.1007/3-540-44745-8_28 fatcat:4wjtfyzuxbei5jaf42au3m6pi4

Matching free trees, maximal cliques, and monotone game dynamics

M. Pelillo
2002 IEEE Transactions on Pattern Analysis and Machine Intelligence  
are in one-to-one correspondence with maximal common subtrees.  ...  Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques  ...  Liu for kindly providing us with the shape database, and the anonymous reviewers for their comments.  ... 
doi:10.1109/tpami.2002.1046176 fatcat:rj6glrcxxfgy7eic4lvlksuyga
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