VF2 Plus: An Improved version of VF2 for Biological Graphs

Carletti, Vincenzo; Foggia, Pasquale; Vento, Mario

doi:10.1007/978-3-319-18224-7_17

Cited by 26 publications

(17 citation statements)

References 18 publications

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“…Improved search orderings for VF2-style algorithms also appear in recent work by Carletti et al (2015) and Carletti (2016), cumulating in VF3 , and by Shen and Zou (2017). We have seen in Section 5 that such an approach could give improvements, but will not bring an algorithm that does not use domains close to the performance of one that does on harder instances.…”

Section: Other Implicationsmentioning

confidence: 79%

“…We illustrate both variants in Figure 1. Although these problems are NP-complete (Garey & Johnson, 1979), modern subgraph isomorphism algorithms based upon constraint programming techniques can handle problem instances with many hundreds of vertices in the pattern graph, and up to ten thousand vertices in the target graph (Solnon, 2010;Audemard, Lecoutre, Modeliar, Goncalves, & Porumbel, 2014;McCreesh & Prosser, 2015;Kotthoff, McCreesh, & Solnon, 2016), and subgraph isomorphism is used successfully in application areas including computer vision (Damiand, Solnon, de la Higuera, Janodet, & Samuel, 2011;Solnon, Damiand, de la Higuera, & Janodet, 2015), biochemistry (Giugno, Bonnici, Bombieri, Pulvirenti, Ferro, & Shasha, 2013;Carletti, Foggia, & Vento, 2015), and pattern recognition Figure 1: On the left, an induced subgraph isomorphism. On the right, a non-induced subgraph isomorphism: the extra dashed edge is not present in the pattern graph.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

McCreesh¹,

Prosser²,

Solnon³

et al. 2018

jair

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The subgraph isomorphism problem involves deciding whether a copy of a pattern graph occurs inside a larger target graph. The non-induced version allows extra edges in the target, whilst the induced version does not. Although both variants are NP-complete, algorithms inspired by constraint programming can operate comfortably on many real-world problem instances with thousands of vertices. However, they cannot handle arbitrary instances of this size. 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 vertices. For the non-induced version of the problem, these instances lie on a satisfiable / unsatisfiable phase transition, whose location we can predict; for the induced variant, much richer behaviour is observed, and constrainedness gives a better measure of difficulty than does proximity to a phase transition. These results have practical consequences: we explain why the widely researched "filter / verify" indexing technique used in graph databases is founded upon a misunderstanding of the empirical hardness of NP-complete problems, and cannot be beneficial when paired with any reasonable subgraph isomorphism algorithm.

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Section: Other Implicationsmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

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

McCreesh¹,

Prosser²,

Solnon³

et al. 2018

jair

View full text Add to dashboard Cite

show abstract

“…VF2 explores the search space starting from the neighbors of each matched query vertex. VF2Plus [11] improves the ordering of VF2 by picking the query vertices with the lowest chance of finding matches in the data graph and the highest number of neighbors among prior vertices in the ordering. VF3 [10] also improves VF2 by proposing heuristics for reducing the search space size and the time of processing each state.…”

Section: Structural Graph Pattern Matchingmentioning

confidence: 99%

A Survey on Distributed Graph Pattern Matching in Massive Graphs

et al. 2021

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Besides its NP-completeness, the strict constraints of subgraph isomorphism are making it impractical for graph pattern matching (GPM) in the context of big data. As a result, relaxed GPM models have emerged as they yield interesting results in a polynomial time. However, massive graphs generated by mostly social networks require a distributed storing and processing of the data over multiple machines, thus, requiring GPM to be revised by adopting new paradigms of big graphs processing, e.g., Think-Like-A-Vertex and its derivatives. This article discusses and proposes a classification of distributed GPM approaches with a narrow focus on the relaxed models.

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“…Most of these algorithms use backtracking to move through the built search tree and find appropriate combination of corresponding vertices of the source graph and the graph-pattern. Algorithms in this class include Ullmann algorithm [19], VF2 [20] (and also VF2 Plus [21] and VF3 [22]), TurboISO [23], CFL-Match [24], QuickSI [25], SPath [26] and others. These algorithms implement various techniques to decrease time needed for the matching process.…”

Section: Related Workmentioning

confidence: 99%

A Multilayer Approach to Subgraph Matching in HP-graphs

Suvorov¹,

Lyadova²

2021

Proceedings of ISP RAS

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Visual modeling is widely used nowadays, but the existing modeling platforms cannot meet all the user requirements. Visual languages are usually based on graph models, but the graph types used have significant restrictions. A new graph model, called HP-graph, whose main element is a set of poles, the subsets of which are combined into vertices and edges, has been previously presented to solve the problem of insufficient expressiveness of the existing graph models. Transformations and many other operations on visual models face a problem of subgraph matching, which slows down their execution. A multilayer approach to subgraph matching can be a solution for this problem if a modeling system is based on the HP-graph. In this case, the search is started on the higher level of the graph model, where vertices and hyperedges are compared without revealing their structures, and only when a candidate is found, it moves to the level of poles, where the comparison of the decomposed structures is performed. The description of the idea of the multilayer approach is given. A backtracking algorithm based on this approach is presented. The Ullmann algorithm and VF2 are adapted to this approach and are analyzed for complexity. The proposed approach incrementally decreases the search field of the backtracking algorithm and helps to decrease its overall complexity. The paper proves that the existing subgraph matching algorithms except ones that modify a graph pattern can be successfully adapted to the proposed approach.

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VF2 Plus: An Improved version of VF2 for Biological Graphs

Cited by 26 publications

References 18 publications

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

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

A Survey on Distributed Graph Pattern Matching in Massive Graphs

A Multilayer Approach to Subgraph Matching in HP-graphs

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