A note on the derivation of maximal common subgraphs of two directed or undirected graphs

Substructure similarity search is to retrieve graphs that approximately contain a given query graph. It has many applications, e.g., detecting similar functions among chemical compounds. The problem is challenging as even testing subgraph containment between two graphs is NP-complete. Hence, existing techniques adopt the filtering-and-verification framework with the focus on developing effective and efficient techniques to remove non-promising graphs.Nevertheless, existing filtering techniques may be still unable to effectively remove many "low" quality candidates.To resolve this, in this paper we propose a novel indexing technique, GrafD-Index, to index graphs according to their "distances" to features. We characterize a tight condition under which the distance-based triangular inequality holds. We then develop lower and upper bounding techniques that exploit the GrafD-Index to (1) prune non-promising graphs and (2) include graphs whose similarities are guaranteed to exceed the given similarity threshold. Considering that the verification phase is not well studied and plays the dominant role in the whole process, we devise efficient algorithms to verify candidates. A comprehensive experiment using real datasets demonstrates that our proposed methods significantly outperform existing methods.

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“…Related work may be found in [1,2,3,4,7,8,16,14,17]. These techniques are not applicable to MCCS detection.…”

Section: Related Workmentioning

confidence: 99%

Connected substructure similarity search

Shang

Lin

Zhang

et al. 2010

Proceedings of the 2010 ACM SIGMOD International Conference on Management of Data

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“…In Definition 3, G C can be computed based on maximal clique detection. 19 In GDM(), the possible operands are any types of graphs (i.e., BG, RAG or STRG).…”

Section: Gdm()mentioning

confidence: 99%

<title>STRG-QL: spatio-temporal region graph query language for video databases</title>

Lee

Çelebi

2008

SPIE Proceedings

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In this paper, we present a new graph-based query language and its query processing for a Graph-based Video Database Management System (GVDBMS). Although extensive researches have proposed various query languages for video databases, most of them have the limitation in handling general-purpose video queries. Each method can handle specific data model, query type or application. In order to develop a general-purpose video query language, we first produce Spatio-Temporal Region Graph (STRG) for each video, which represents spatial and temporal information of video objects. An STRG data model is generated from the STRG by exploiting object-oriented model. Based on the STRG data model, we propose a new graph-based query language named STRG-QL, which supports various types of video query. To process the proposed STRG-QL, we introduce a rule-based query optimization that considers the characteristics of video data, i.e., the hierarchical correlations among video segments. The results of our extensive experimental study show that the proposed STRG-QL is promising in terms of accuracy and cost.

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“…For a simple comparison between a pair of chemical graphs consisting of m and n atoms, respectively, the maximum number of possible atom-by-atom comparisons necessary to determine all common subgraphs consisting of k atoms is [32] !…”

Section: Algorithmsmentioning

confidence: 99%

“…It appears that Levi [32], later used by Cone [10] in a chemical context, was the first to suggest reducing the MCIS problem to the maximum clique problem in the published literature, but it has been independently discovered by numerous authors, including Barrow and Burstall [34] and Vizing [35]. In a related work, Kozen transformed the problem of isomorphism to clique detection in a compatibility graph that he labeled an M-graph [36].…”

Section: Maximum Clique-based Algorithmmentioning

confidence: 99%

“…In their definition a vertex in a graph corresponds to a superatom which can be one of a predefined number of ring systems, functional groups, or alkyl chains, and an edge exists in the graph if a pair of superatoms are adjacent in the molecular structure. In their experiments, the Levi [32] MCIS algorithm as adapted by Cone et al [10] was used. Takahashi et.…”

Section: Problem Reductionmentioning

confidence: 99%

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Untitled

Raymond

Willett

2002

Journal of Computer-Aided Molecular Design

340

118

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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. This paper provides a classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and makes recommendations regarding their applicability to typical chemoinformatics tasks.

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A note on the derivation of maximal common subgraphs of two directed or undirected graphs

Cited by 201 publications

References 9 publications

Connected substructure similarity search

Connected substructure similarity search

<title>STRG-QL: spatio-temporal region graph query language for video databases</title>

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