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Backtrack search algorithms and the maximal common subgraph problem

James J. McGregor
1982 Software, Practice & Experience  
Techniques available in this application area for ordering and pruning the backtrack search are discussed.  ...  An efficient but readable version of such an algorithm is presented and its use in the problem of finding the maximal common subgraph of two graphs is described.  ...  We will introduce a maximal common subgraph algorithm that uses a backtrack search' as its basic component. Backtrack search, if used alone in a problem of this nature, is grotesquely inefficient.  ... 
doi:10.1002/spe.4380120103 fatcat:3zi626ejsvdwrgwbsjkc6jpajq

The Glasgow Subgraph Solver: Using Constraint Programming to Tackle Hard Subgraph Isomorphism Problem Variants [chapter]

Ciaran McCreesh, Patrick Prosser, James Trimble
2020 Lecture Notes in Computer Science  
The Glasgow Subgraph Solver provides an implementation of state of the art algorithms for subgraph isomorphism problems.  ...  found to be computationally hard by other solvers.  ...  This work was supported by the Engineering and Physical Sciences Research Council (grant numbers EP/P026842/1, EP/M508056/1, and EP/N007565).  ... 
doi:10.1007/978-3-030-51372-6_19 fatcat:orm2rsy5obabnfkb34fghx7gv4

Finding Maximum Common Connected Subgraphs Using Clique Detection or Constraint Satisfaction Algorithms [chapter]

Philippe Vismara, Benoît Valery
2008 Communications in Computer and Information Science  
This paper investigates the problem of Maximum Common Connected Subgraph (MCCS) which is not necessarily an induced subgraph.  ...  This problem has so far been neglected by the literature which is mainly devoted to the MCIS problem.  ...  Given two graphs G1 and G2, a Common Connected Subgraphs (CCS) of G1 and G2 is a connected graph H isomorphic to both subgraphs of G1 and G2.  ... 
doi:10.1007/978-3-540-87477-5_39 fatcat:yjfdlsjdrzfbboo2x7mvtjwb5i

Distributed Subgraph Enumeration via Backtracking-based Framework [article]

Zhaokang Wang, Weiwei Hu, Chunfeng Yuan, Rong Gu, Yihua Huang
2020 arXiv   pre-print
Each task enumerates subgraphs around a vertex in the data graph, guided by a backtracking-based execution plan. B-BENU does not shuffle any partial matching result.  ...  and fraud detection.  ...  Backtracking-based Framework The backtracking-based framework is popular among serial subgraph isomorphism algorithms.  ... 
arXiv:2006.12819v3 fatcat:orfdrbgyozcjrowlsdambm4c5q

Maximum common subgraph isomorphism algorithms for the matching of chemical structures

John W Raymond, Peter Willett
2002 Journal of Computer-Aided Molecular Design  
The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures.  ...  A graph G 12 is a common induced subgraph of graphs G 1 and G 2 if G 12 is isomorphic to induced subgraphs of G 1 and G 2 .  ...  Both these methods essentially just require that any vertex added to a common subgraph during clique detection must be connected to at least one other vertex in the currently detected common subgraph when  ... 
pmid:12510884 fatcat:hp6jkd6b3ncx7ixyefiqk77yxq

Efficient subgraph isomorphism detection: a decomposition approach

B.T. Messmer, H. Bunke
2000 IEEE Transactions on Knowledge and Data Engineering  
In this paper, we propose a new algorithm for subgraph isomorphism detection from a set of a priori known model graphs to an input graph that is given online.  ...  Subgraphs that appear multiple times within the same or within different model graphs are represented only once, thus reducing the computational effort to detect them in an input graph.  ...  ACKNOWLEDGMENTS This work is part of a project of the Priority Program SPP IF, No. 5003-34285, funded by the Swiss National Science Foundation.  ... 
doi:10.1109/69.842269 fatcat:biqadkuxfbecdnlvc6vi7ggnwe

A New Method for Motif Mining in Biological Networks

Yuan Xu, Qiang Zhang, Changjun Zhou
2014 Evolutionary Bioinformatics  
First, all sub-graphs can be enumerated by adding edges and nodes progressively, using the backtracking method based on the associated matrix.  ...  CopYRight: © the authors, publisher and licensee libertas academica limited. this is an open-access article distributed under the terms of the creative commons cc-By-nc 3.0 license.  ...  These instances for testing the algorithm are up-todate versions of the motif detection tests used by other existing algorithms.  ... 
doi:10.4137/ebo.s15207 pmid:25336896 pmcid:PMC4196890 fatcat:2pvlc3dguvhsjbb7yptkw6dapu

Mining Minimal Contrast Subgraph Patterns [chapter]

Roger Ming Hieng Ting, James Bailey
2006 Proceedings of the 2006 SIAM International Conference on Data Mining  
However, mining minimal contrast subgraphs is a challenging task, due to the exponentially large search space and graph (sub)isomorphism problems.  ...  We present an algorithm which utilises a backtracking tree to first compute the maximal common edge sets and then uses a minimal hypergraph transversal algorithm, to derive the set of minimal contrast  ...  Acknowledgements: This work is partially supported by National ICT Australia.  ... 
doi:10.1137/1.9781611972764.76 dblp:conf/sdm/TingB06 fatcat:xj6zum233vg2lp2k75zz2przk4

A Comparison of Algorithms for Maximum Common Subgraph on Randomly Connected Graphs [chapter]

Horst Bunke, Pasquale Foggia, Corrado Guidobaldi, Carlo Sansone, Mario Vento
2002 Lecture Notes in Computer Science  
In this paper, two exact algorithms for maximum common subgraph detection are described.  ...  A graph g is called a maximum common subgraph of two graphs, g 1 and g 2 , if there exists no other common subgraph of g 1 and g 2 that has more nodes than g.  ...  Fig. 1 : 1 Sketch of the space state search for maximum common subgraph detection. Fig. 2 : 2 Sketch of the maximum clique detection algorithm.  ... 
doi:10.1007/3-540-70659-3_12 fatcat:ky4xyusn4zc27nnwqcr5twwcve

Mining frequent subgraphs in multigraphs

Vijay Ingalalli, Dino Ienco, Pascal Poncelet
2018 Information Sciences  
experiments reveal two things: MuGraM discovers multigraph patterns, where other existing approaches are unable to do so; MuGraM, when applied to simple graphs, outperforms the state of the art approaches by  ...  MuGraM e ciently performs the task of subgraph matching, which is crucial for support measure, and further leverages several optimization techniques for swift discovery of frequent subgraphs.  ...  Acknowledgments This work has been funded by LabEx NUMEV integrated into the I-SITE MUSE (ANR-10-LABX-20).  ... 
doi:10.1016/j.ins.2018.04.001 fatcat:zinpz6rjgrdxtpkjmvwwfoxjuq

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John W. Raymond, Peter Willett
2012 Journal of Computer-Aided Molecular Design  
The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures.  ...  A graph G 12 is a common induced subgraph of graphs G 1 and G 2 if G 12 is isomorphic to induced subgraphs of G 1 and G 2 .  ...  Both these methods essentially just require that any vertex added to a common subgraph during clique detection must be connected to at least one other vertex in the currently detected common subgraph when  ... 
doi:10.1023/a:1021271615909 fatcat:ext5jemfjrejhjovknhbbtn64q

Similarity search on supergraph containment

Haichuan Shang, Ke Zhu, Xuemin Lin, Ying Zhang, Ryutaro Ichise
2010 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010)  
A supergraph containment search is to retrieve the data graphs contained by a query graph.  ...  In this paper, we study the problem of efficiently retrieving all data graphs approximately contained by a query graph, namely similarity search on supergraph containment.  ...  Different from the maximum clique paradigm, the backtracking technique searches the maximum common subgraph by enumerate all common subgraphs of the two given graphs and choosing the largest one.  ... 
doi:10.1109/icde.2010.5447846 dblp:conf/icde/ShangZLZI10 fatcat:2ht3nsb7xzcjxkjxs52qif4p64

Subgraph Matching via Query-Conditioned Subgraph Matching Neural Networks and Bi-Level Tree Search [article]

Yunsheng Bai, Derek Xu, Yizhou Sun, Wei Wang
2022 arXiv   pre-print
This task is called Subgraph Matching which essentially performs subgraph isomorphism check between a query graph and a large target graph.  ...  However, for the specific task of Subgraph Matching, though the query graph is usually small given by the user as input, the target graph is often orders-of-magnitude larger.  ...  C Comparison with Maximum Common Subgraph (MCS) Detection Subgraph Matching and MCS detection are highly related tasks, and one can convert Subgraph Matching to MCS detection by feeding the input (q, G  ... 
arXiv:2207.10305v1 fatcat:zip77zrwsngvxm46uypga45yt4

Demadroid: Object Reference Graph-Based Malware Detection in Android

Huanran Wang, Hui He, Weizhe Zhang
2018 Security and Communication Networks  
Motivated by this, we present Demadroid, a framework to implement the detection of Android malware.  ...  The VF algorithm proposed by Cordellac [27] is applied to both isomorphism and subgraph isomorphism. Cordellac defined a heuristic search by analyzing the adjacent nodes of matched nodes.  ...  It is also used to find the largest subgraph match, which is called the maximum common subgraph (MCS). Analysis of the Subgraph Isomorphism Matching Algorithm.  ... 
doi:10.1155/2018/7064131 fatcat:cqkeiaa5wbfpdeszncvaunpinu

Classification of some strongly regular subgraphs of the McLaughlin graph

J. Degraer, K. Coolsaet
2008 Discrete Mathematics  
By means of an exhaustive computer search we have proved that the strongly regular graphs with parameters (v, k, , ) = (105, 32, 4, 12), (120, 42, 8, 18) and (176, 70, 18, 34) are unique up to isomorphism  ...  Each of these graphs occurs as an induced subgraph in the strongly regular McLaughlin graph.  ...  (v, Isomorphism rejection In order to detect partially filled matrices that are isomorphic to partially filled matrices considered earlier in the search we use a so-called orderly approach.  ... 
doi:10.1016/j.disc.2006.11.055 fatcat:pch4efl275aspnx3rde5e5sr7q
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