Challenging Complexity of Maximum Common Subgraph Detection Algorithms: A Performance Analysis of Three Algorithms on a Wide Database of Graphs

Conte, Donatello; Foggia, Pasquale; Vento, Mario

doi:10.7155/jgaa.00139

Cited by 66 publications

(42 citation statements)

References 30 publications

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“…Previous experimental evaluations of the association graph model have used either maximal clique enumeration algorithms [22,54] (even when the maximisation problem was being considered), or very simple maximum clique algorithms [6,8], and so their conclusions may now be overly pessimistic. Thus we re-evaluate the approach using a modern maximum clique algorithm.…”

Section: Re-evaluating the Clique Model For Mcsmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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Abstract. The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

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Section: Re-evaluating the Clique Model For Mcsmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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“…Finding the MCS in random graphs is an NP-complete problem [3,4,5]. There are mainly two algorithms that can find the MCS in two arbitrary selected graphs: 1) The algorithm by McGregor that uses a state space representation, and 2) the Durand-Pasari algorithm that is based on an association graph and clique detection in it [3,4,6].…”

Section: Related Workmentioning

confidence: 99%

“…However, their performance strongly depends on the type and properties of graph used. The size of the graphs analyzed is usually limited from 25 to 1000 vertices [3,4,6,7].…”

Section: Related Workmentioning

confidence: 99%

An Approximate Maximum Common Subgraph Algorithm for Large Digital Circuits

Rutgers

Wolkotte

Hölzenspies

et al. 2010

2010 13th Euromicro Conference on Digital System Design: Architectures, Methods and Tools

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Abstract-This paper presents an approximate Maximum Common Subgraph (MCS) algorithm, specifically for directed, cyclic graphs representing digital circuits. Because of the application domain, the graphs have nice properties: they are very sparse; have many different labels; and most vertices have only one predecessor. The algorithm iterates over all vertices once and uses heuristics to find the MCS. It is linear in computational complexity with respect to the size of the graph. Experiments show that very large common subgraphs were found in graphs of up to 200,000 vertices within a few minutes, when a quarter or less of the graphs differ. The variation in run-time and quality of the result is low.

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“…Standard maximum common subgraph algorithms are relatively simple to implement, but have high computational complexity, being NP-complete [4]. Hence our investigation of small graphs.…”

Section: A Graph Edit Distance Fitness Functionmentioning

confidence: 99%

Representation and structural biases in CGP

Payne

Stepney

2009

2009 IEEE Congress on Evolutionary Computation

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Abstract-An evolutionary algorithm automatically discovers suitable solutions to a problem, which may lie anywhere in a large search space of candidate solutions. In the case of Genetic Programming, this means performing an efficient search of all possible computer programs represented as trees. Exploration of the search space appears to be constrained by structural mechanisms that exist in Genetic Programming as a consequence of using trees to represent solutions. As a result, programs with certain structures are more likely to be evolved, and others extremely unlikely.We investigate whether the graph representation used in Cartesian Genetic Programming causes an analogous biasing effect, imposing natural limitations on the class of solution structures that are likely to be evolved. Representation bias and structural bias are identified: the rarer "regular" structures appear to be easier to evolve than more common "irregular" ones.

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Challenging Complexity of Maximum Common Subgraph Detection Algorithms: A Performance Analysis of Three Algorithms on a Wide Database of Graphs

Cited by 66 publications

References 30 publications

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

An Approximate Maximum Common Subgraph Algorithm for Large Digital Circuits

Representation and structural biases in CGP

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