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When Subgraph Isomorphism is Really Hard, and Why This Matters for Graph Databases

Ciaran McCreesh, Patrick Prosser, Christine Solnon, James Trimble
2018 The Journal of Artificial Intelligence Research  
We show how to generate "really hard" random instances for subgraph isomorphism problems, which are computationally challenging with a couple of hundred vertices in the target, and only twenty pattern  ...  of NP-complete problems, and cannot be beneficial when paired with any reasonable subgraph isomorphism algorithm.  ...  We are grateful to Iva Babukova for her help with the datasets and for sharing the results of her experiments.  ... 
doi:10.1613/jair.5768 fatcat:wyevxjttzjabpgwqb23nlyb6n4

Spectral recognition of graphs

Dragos Cvetkovic
2012 Yugoslav Journal of Operations Research  
networks in bio-informatics, recognizing hard instances for combinatorial optimization problems such as the travelling salesman problem).  ...  Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found.  ...  This work is supported by the Serbian Ministry for Education and Science, Grants ON174033 and III44006.  ... 
doi:10.2298/yjor120925025c fatcat:grql72fepvearizxhgm4slhlwa

Constraint-Based Graph Matching [chapter]

Vianney le Clément, Yves Deville, Christine Solnon
2009 Lecture Notes in Computer Science  
Depending on the measure characteristics, this program either uses CP -which is better suited for computing exact measures such as (sub)graph isomorphism-or CBLS -which is better suited for computing error-tolerant  ...  This language is designed on top of Comet, a programming language supporting both Constraint Programming (CP) and Constraint-Based Local Search (CBLS).  ...  Acknowledgments The authors want to thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1007/978-3-642-04244-7_23 fatcat:sz7orbrbyjfvlonzga64jnjpgm

Reactive Tabu Search for Measuring Graph Similarity [chapter]

Sébastien Sorlin, Christine Solnon
2005 Lecture Notes in Computer Science  
Graph matching is often used for image recognition.  ...  In a second part, we address the problem of computing this measure and we describe two algorithms: a greedy algorithm, that quickly computes sub-optimal solutions, and a reactive Tabu search algorithm,  ...  The 14 last instances appeared to be really hard ones, that needed more than 25, 000 moves to be solved.  ... 
doi:10.1007/978-3-540-31988-7_16 fatcat:jcn7qvae3vgs3nffyqsijjoyfq

A Strengthened Branch and Bound Algorithm for the Maximum Common (Connected) Subgraph Problem [article]

Jianrong Zhou and Kun He and Jiongzhi Zheng and Chu-Min Li and Yanli Liu
2022 arXiv   pre-print
We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union  ...  Given two graphs for which we search for the maximum common (connected) induced subgraph, the first operator of LSM maintains a score for the branching node using the short-term reward of each vertex of  ...  As an NP-hard problem, MCS is computationally very challenging.  ... 
arXiv:2201.06252v1 fatcat:e5t4qyvmqnedbkv5x2stey4p34

Memetic algorithms for inexact graph matching

Thomas Barecke, Marcin Detyniecki
2007 2007 IEEE Congress on Evolutionary Computation  
We show that permutation encoding is robust enough to allow addressing both, the matching problem for graphs of the same size, and the subgraph matching problem.  ...  The noise-robust matching of two graphs is a hard combinatorial problem with practical importance in several domains.  ...  Moreover, the error-correcting subgraph isomorphism problem also aims to minimize Eq. 4, but this time for graphs of different sizes.  ... 
doi:10.1109/cec.2007.4425024 dblp:conf/cec/BareckeD07 fatcat:aooxlmekt5asrimsnke3ntat5u

Experimental Evaluation of Subgraph Isomorphism Solvers [chapter]

Christine Solnon
2019 Lecture Notes in Computer Science  
Subgraph Isomorphism (SI) is an NP-complete problem which is at the heart of many structural pattern recognition tasks as it involves finding a copy of a pattern graph into a target graph.  ...  or LAD, and they are clearly outperformed by Glasgow on hard instances.  ...  Introduction Subgraph Isomorphism (SI) is an NP-complete problem which involves finding a copy of a pattern graph into a target graph, i.e., finding a mapping that associates a different target node to  ... 
doi:10.1007/978-3-030-20081-7_1 fatcat:6rkyuov5ozfkzmevvfmvoaguzq

Comparing stars

Zhiping Zeng, Anthony K. H. Tung, Jianyong Wang, Jianhua Feng, Lizhu Zhou
2009 Proceedings of the VLDB Endowment  
Unfortunately, the problem of graph edit distance computation is NP-Hard in general.  ...  Graph data have become ubiquitous and manipulating them based on similarity is essential for many applications.  ...  For two graphs g1 and g2, if |V1| > |V2| or |E1| > |E2|, we can quickly state that g1 cannot be subgraph isomorphic to g2 because it is impossible to find such a subgraph isomorphism.  ... 
doi:10.14778/1687627.1687631 fatcat:gjpo5ulwljdmpmaae474vke3pm

GLSearch: Maximum Common Subgraph Detection via Learning to Search [article]

Yunsheng Bai, Derek Xu, Yizhou Sun, Wei Wang
2021 arXiv   pre-print
However, MCS computation is NP-hard, and state-of-the-art MCS solvers rely on heuristic search algorithms which in practice cannot find good solution for large graph pairs given a limited computation budget  ...  Detecting the Maximum Common Subgraph (MCS) between two input graphs is fundamental for applications in drug synthesis, malware detection, cloud computing, etc.  ...  A learning based branch and bound for maximum common subgraph problems. IJCAI, 2019. McCreesh, C., Ndiaye, S. N., Prosser, P., and Solnon, C.  ... 
arXiv:2002.03129v3 fatcat:zhvq3sub55ee5i32l5aqs6f2qm

Algorithmic Data Science (Invited Talk)

Petra Mutzel, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
ACM Subject Classification Theory of computation → Design and analysis of algorithms; Theory of computation → Graph algorithms analysis; Theory of computation → Complexity theory and logic; Mathematics  ...  The area of algorithmic data science provides new opportunities for researchers in the algorithmic community.  ...  In particular, the author provides intuition for the presented statistical and mathematical concepts.  ... 
doi:10.4230/lipics.stacs.2019.3 dblp:conf/stacs/Mutzel19 fatcat:4sq6azx2snb2tkhr4n5wchaoyq

The Gn,m Phase Transition is Not Hard for the Hamiltonian Cycle Problem

B. Vandegriend, J. Culberson
1998 The Journal of Artificial Intelligence Research  
We design a set of graphs with a feature our algorithm is unable to detect and so are very hard for our algorithm, but in these we can vary the average degree from O(1) to O(n).  ...  When we consider more regular graphs based on a generalization of knight's tours, we observe frequent instances of really hard graphs, but on these the average degree is bounded by a constant.  ...  Acknowledgements This research w as supported by Natural Sciences and Engineering Research Council Grant No. OGP8053.  ... 
doi:10.1613/jair.512 fatcat:mpvofqezyvbovd25tswy55slbm

A3: An Automatic Topology-Aware Malfunction Detection and Fixation System in Data Center Networks [article]

Che Zhang, Shiwei Zhang, Bo Jin, Weichao Li, Zhen Wang, Qing Li, Yi Wang
2020 arXiv   pre-print
A3 innovatively formulates the problem of finding minimal fixation to the problem of computing minimum graph difference (NP-hard) and solves it in O(k^6) and O(k^3) for any less than k/2 and k/4 undirected  ...  To solve the problems, we design and implement A3, an automatic topology-aware malfunction detection and fixation system.  ...  The SIP is the problem of answering whether a graph H is isomorphic to a subgraph of G. Any SIP instance (G, H) can be reduced to an MCESP instance with a pair of graphs (G, H) and a number |H|.  ... 
arXiv:2001.02163v1 fatcat:i7jfcp2kkrb6llqo26aoa24sj4

Economically Optimal Road Subnetwork

Anna Cerna, Jan Cerny, Vladimir Pribyl
2014 Communications - Scientific Letters of the University of Zilina  
As shown in [27] , both problems 2.1 and 2.2 are NP-hard.  ...  Their second problem is to find the minimum weight-sum subgraph isomorphic to the given graph H.  ... 
doi:10.26552/com.c.2014.2.83-91 fatcat:5yrpsojapzdl5iblaqifj2w7vy

Endgame problems of Sim-like graph Ramsey avoidance games are PSPACE-complete

Wolfgang Slany
2002 Theoretical Computer Science  
The following game variants are also shown to have PSPACE-complete endgame problems: (1) completing a monochromatic subgraph isomorphic to A is forbidden and the player who is ÿrst unable to move loses  ...  Replacing K6 and K3 by arbitrary graphs generalizes Sim to graph Ramsey avoidance games.  ...  I am grateful to the anonymous reviewers of previous versions of this work for their valuable comments.  ... 
doi:10.1016/s0304-3975(01)00179-7 fatcat:lioyx46nzneffh2x2ogfkaogwm

Graph Ramsey games [article]

Wolfgang Slany
1999 arXiv   pre-print
In avoidance games, completing a monochromatic subgraph isomorphic to another graph A leads to immediate defeat or is forbidden and the first player that cannot move loses.  ...  In achievement games, the first player that completes a monochromatic subgraph isomorphic to A wins.  ...  classmates from high-school who competed with me in programming heuristic players for Sim on our various pocket calculators.  ... 
arXiv:cs/9911004v1 fatcat:oita7dv6kverpodkgsgewlmsse
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