Arc Consistency Projection: A New Generalization Relation for Graphs

Liquière, Michel

doi:10.1007/978-3-540-73681-3_25

Cited by 5 publications

(9 citation statements)

References 11 publications

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“…The AC-projection operator [14] differs from these redefinitions of graph and subgraph isomorphism [7,8] regarding the following aspects. First, the AC-projection is not based on a graph distance measure or a threshold during the matching process.…”

Section: Related Work and Discussionmentioning

confidence: 99%

“…These two instances are based on the arc consistency technique. Indeed, these approaches use properties of the AC-projection operator initially introduced in [14].…”

Section: Pattern-growth Strategymentioning

confidence: 99%

“…The approach suggested in [14] advocates a projection operator based on the arc consistency algorithm. This projection method has the required properties: polynomiality, local validation, parallelization, structural interpretation.…”

Section: The Ac-projection Operatormentioning

confidence: 99%

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LC-mine: a framework for frequent subgraph mining with local consistency techniques

et al. 2014

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Developing algorithms that discover all frequently occurring subgraphs in a large graph database is computationally extensive, as graph and subgraph isomorphisms play a key role throughout the computations. Since subgraph isomorphism testing is a hard problem, fragment miners are exponential in runtime. To alleviate the complexity issue, we propose to introduce a bias in the projection operator and instead of using the costly subgraph isomorphism projection, one can use a polynomial projection having a semantically valid structural interpretation. In this paper, our purpose is to present LC-mine, a generic and efficient framework to mine frequent subgraphs by the means of local consistency techniques used in the constraint programming field. Two instances of the framework based on the arc consistency technique are developed and presented in this paper. The first instance follows a breadthfirst order, while the second is a pattern-growth approach that follows a depth-first search space exploration strategy. Then, we prove experimentally that we can achieve an important performance gain without or with nonsignificant loss of discovered patterns in terms of quality.

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Section: Related Work and Discussionmentioning

confidence: 99%

“…These two instances are based on the arc consistency technique. Indeed, these approaches use properties of the AC-projection operator initially introduced in [14].…”

Section: Pattern-growth Strategymentioning

confidence: 99%

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LC-mine: a framework for frequent subgraph mining with local consistency techniques

et al. 2014

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“…12, the author introduced an interesting projection operator named ACprojection which seems to have good properties and ensure polynomial time and memory consumption. The forthcoming sections present this operator with its many interesting properties and show an optimized algorithm for computing it.…”

Section: Critical Discussionmentioning

confidence: 99%

“…Then, we present the AC-projection operator initially introduced in Ref. 12, as well as its very interesting properties. We propose an efficient graph mining algorithm using the AC-projection operator.…”

Section: Introductionmentioning

confidence: 99%

A Projection Bias in Frequent Subgraph Mining Can Make a Difference

Douar

Latiri

Liquière

et al. 2014

Int. J. Artif. Intell. Tools

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International audienceThe aim of the frequent subgraph mining task is to find frequently occurring subgraphs in a large graph database. However, this task is a thriving challenge, as graph and subgraph isomorphisms play a key role throughout the computations. Since subgraph isomorphism testing is a hard problem, subgraph miners are exponential in runtime. To alleviate the complexity issue, we propose to introduce a bias in the projection operator and instead of using the costly subgraph isomorphism projection, one can use a polynomial projection having a semantically-valid structural interpretation. This paper presents a new projection operator for graphs named AC-projection, which exhibits nice theoretical complexity properties. We study the size of the search space as well as some practical properties of the projection operator. We also introduce a novel breadth-first algorithm for frequent AC-reduced subgraphs mining. Then, we prove experimentally that we can achieve an important performance gain (polynomial complexity projection) without or with non-significant loss of discovered patterns in terms of quality

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Graph-Based Relational Learning with a Polynomial Time Projection Algorithm

Douar

Liquière

Latiri

et al. 2012

Inductive Logic Programming

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The paper presents a new projection operator for graphs, named AC-projection, which exhibits good complexity properties as opposed to the graph isomorphism (Θ-subsumption) operator typically used in graph mining. We study the size of the search space and some practical properties of the projection operator. These properties give us a specialization algorithm using simple local operations. Then we prove experimentally that we can achieve an important performance gain (polynomial complexity projection) without or with non-significant loss of discovered patterns quality.

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Arc Consistency Projection: A New Generalization Relation for Graphs

Cited by 5 publications

References 11 publications

LC-mine: a framework for frequent subgraph mining with local consistency techniques

LC-mine: a framework for frequent subgraph mining with local consistency techniques

A Projection Bias in Frequent Subgraph Mining Can Make a Difference

Graph-Based Relational Learning with a Polynomial Time Projection Algorithm

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