Graph pattern matching with counting quantifiers and label-repetition constraints

Mahfoud, Houari

doi:10.1007/s10586-019-02977-3

Cited by 9 publications

(6 citation statements)

References 28 publications

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“…C , and L(e v ) = L C (e u )}. We have shown in [14] that the checking of C ≺ c G as well as the computation of the maximum match relation S G…”

Section: Conditional Graph Pattern Matchingmentioning

confidence: 99%

“…When considering data and patterns modeled as graphs, evaluating a graph pattern Q 2 over a data graph G by simulation [16] and all its variants [2,[11][12][13][14] yields a match result defined as a function that maps each node (resp. edge) of Q 2 to all its matches in G. Therefore, we revise the traditional definition of containment for CGPs in terms of match result as follows.…”

Section: Definition and Checkingmentioning

confidence: 99%

“…However, existing simulation-based GPM consider very simple patterns which do not meet requirements of real-life applications. To overcome this limit, we proposed in [14] conditional graph patterns (CGPs) which allow to query data graphs with complex features like quantifications, predicates and negation. Our goal is to study the containment problem of CGPs in order to reduce their matching time.…”

Section: Introductionmentioning

confidence: 99%

“…Contributions and Road-map. We first recall from [14,15] the definition of CGPs and we show how they can be matched in quadratic time using conditional simulation (Section 3). Next, we make the following contributions.…”

Section: Introductionmentioning

confidence: 99%

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Revisited Containment for Graph Patterns

Mahfoud¹

2022

Preprint

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We consider the class of conditional graph patterns (CGPs) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider matching of CGPs under simulation semantics which can be conducted in quadratic time. In emerging applications, one would like to reduce more this matching time, and the static analysis of patterns may allow ensuring part of this reduction. We study the containment problem of CGPs that aims to check whether the matches of some pattern P1, over any data graph, are contained in those of another pattern P2 (written P1 ⊑ P2). The optimization process consists to extract matches of P1 only from those of P2 without querying the (possibly large) data graph. We show that the traditional semantics of containment is decidable in quadratic time, but it fails to meet the optimization goal in the presence of negation and predicates. To overcome this limit, we propose a new semantics of containment, called strong containment, that is more suitable for CGPs and allows to reduce their matching time. We show that strong containment can be decided in cubic time by providing such an algorithm. We are planing to use results of this paper to answer CGPs using views. This paper is part of an ongoing project that aims to design a caching system for complex graph patterns.

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“…C , and L(e v ) = L C (e u )}. We have shown in [14] that the checking of C ≺ c G as well as the computation of the maximum match relation S G…”

Section: Conditional Graph Pattern Matchingmentioning

confidence: 99%

Section: Definition and Checkingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Revisited Containment for Graph Patterns

Mahfoud¹

2022

Preprint

Self Cite

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“…A couple ( u , v ) is deleted from if there exists a predicate q defined over u in Q where: q is positive but the ball centered at v in G , , does not match it (lines 4–6); or q is negative but it is matched by the ball (lines 7–9). As remarked in [ 17 ], when a couple ( u , v ) is deleted from (lines 5 + 8), other couples in may become incorrect w.r.t constraints. For this reason, after deleting all couples of that are incorrect w.r.t predicates of Q (lines 4–9), we refine again the match relation to keep only matches that are correct w.r.t constraints (line 10).…”

Section: An Algorithm For Cgps Matchingmentioning

confidence: 99%

Conditional Graph Pattern Matching with a Basic Static Analysis

Mahfoud

2021

Pattern Recognition and Artificial Intelligence

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We propose conditional graph patterns ( CGPs ) that extend conventional ones with simple counting quantifiers on edges, attributes on nodes, positive and negative predicates. In emerging applications such as social network marketing, CGPs allow to express complex search conditions and to find more sensible information than their traditional counterparts. We show that the CGPs expressivity does not come with a much higher price. Indeed, we propose a matching algorithm that is based on a revised notion of graph simulation and allows to match CGPs over any data graphs in quadratic time, as opposed to the prohibitive solutions based on subgraph isomorphism. We discuss a parallel version of our algorithm that makes it very efficient over real-life data. We investigate the satisfiability and containment problems of CGPs and we show that they are in quadratic time by providing a non-trivial checking algorithm for each one. This paper is the first effort that investigates static analysis of non-conventional graph patterns containing important features that are widely used in practice. An extensive experimental study has been conducted to show effectiveness and efficiency of our results.

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Graph Pattern Matching Preserving Label-Repetition Constraints

Mahfoud

2018

Lecture Notes in Computer Science

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Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete.To lower its complexity, many extensions of graph simulation have been proposed which focus on some topological constraints of pattern graphs that can be preserved in polynomial-time over data graphs. We discuss in this paper the satisfaction of a new topological constraint, called Label-Repetition constraint. To the best of our knowledge, existing polynomial approaches fail to preserve this constraint, and moreover, one can adopt only subgraph isomorphism for this end which is cost-prohibitive. We present first a necessary and sufficient condition that a data subgraph must satisfy to preserve the Label-Repetition constraints of the pattern graph. Furthermore, we define matching based on a notion of triple simulation, an extension of graph simulation by considering the new topological constraint. We show that with this extension, graph pattern matching can be performed in polynomial-time, by providing such an algorithm. Our algorithm is sub-quadratic in the size of data graphs only, and quartic in general. We show that our results can be combined with orthogonal approaches for more expressive graph pattern matching. ACM Subject ClassificationF.2 [Analysis of algorithms and problem complexity]: Nonnumerical algorithms and problems[pattern matching] . Finding replicated web collections. In Proc. of SIGMOD, pages 355-366, 2000. 2 Gao Cong, Wenfei Fan, and Anastasios Kementsietsidis. Distributed query evaluation with performance guarantees. In Proc. of SIGMOD, pages 509-520, 2007. 3 Luigi P. Cordella, Pasquale Foggia, Carlo Sansone, and Mario Vento. A (sub)graph isomorphism algorithm for matching large graphs.

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Graph pattern matching with counting quantifiers and label-repetition constraints

Cited by 9 publications

References 28 publications

Revisited Containment for Graph Patterns

Revisited Containment for Graph Patterns

Conditional Graph Pattern Matching with a Basic Static Analysis

Graph Pattern Matching Preserving Label-Repetition Constraints

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