A large database of graphs and its use for benchmarking graph isomorphism algorithms

Santo, Massimo De; Foggia, Pasquale; Sansone, Carlo; Vento, Mario

doi:10.1016/s0167-8655(02)00253-2

Cited by 65 publications

(51 citation statements)

References 9 publications

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“…-Classes 4 to 8 contain randomly generated graphs from a database of graphs commonly used for benchmarking subgraph isomorphism algorithms [7]: boundeddegree graphs for classes 4 and 5, regular meshes for classes 6 and 7, and random graphs with uniform edge probabilities for class 8. All of these instances are satisfiable.…”

Section: Problem Instancesmentioning

confidence: 99%

Portfolios of Subgraph Isomorphism Algorithms

Kotthoff

McCreesh

Solnon

2016

Lecture Notes in Computer Science

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Abstract. Subgraph isomorphism is a computationally challenging problem with important practical applications, for example in computer vision, biochemistry, and model checking. There are a number of state-of-the-art algorithms for solving the problem, each of which has its own performance characteristics. As with many other hard problems, the single best choice of algorithm overall is rarely the best algorithm on an instance-by-instance. We develop an algorithm selection approach which leverages novel features to characterise subgraph isomorphism problems and dynamically decides which algorithm to use on a per-instance basis. We demonstrate substantial performance improvements on a large set of hard benchmark problems. In addition, we show how algorithm selection models can be leveraged to gain new insights into what affects the performance of an algorithm.

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Section: Problem Instancesmentioning

confidence: 99%

Portfolios of Subgraph Isomorphism Algorithms

Kotthoff

McCreesh

Solnon

2016

Lecture Notes in Computer Science

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“…The MIVIA (formerly SIVA) laboratory ARG graph database [18] is one of the most extensive publicly-available databases for graph matching. It contains synthetically-generated matched pairs for graph and subgraph isomorphism.…”

Section: Graph Datasetmentioning

confidence: 99%

“…1 The term irregularity in Table 2 refers to the relocation of edges in the graphs, such that they no longer perfectly adhere to their type category. A comprehensive explanation of the full dataset and parameters is available in [33,18].…”

Section: Graph Datasetmentioning

confidence: 99%

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Efficient subgraph matching using topological node feature constraints

Dahm

Bunke

Caelli

et al. 2015

Pattern Recognition

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a b s t r a c tThis paper presents techniques designed to minimise the number of states which are explored during subgraph isomorphism detection. A set of advanced topological node features, calculated from nneighbourhood graphs, is presented and shown to outperform existing features. Further, the pruning effectiveness of both the new and existing topological node features is significantly improved through the introduction of strengthening techniques. In addition to topological node features, these strengthening techniques can also be used to enhance application-specific node labels using a proposed novel extension to existing pruning algorithms. Through the combination of these techniques, the number of explored search states can be reduced to near-optimal levels.

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“…In the literature, error-tolerant GM methods have often been evaluated in a classification context and less deeply assessed in terms of the accuracy of the found solution when scaling up to match large graphs [12,1,4,5,3]. To evaluate the accuracy of error-tolerant GM methods, graph-level information is required at matching level (i.e., matching quality and similarity deviation) and not only at class level.…”

mentioning

confidence: 99%

Anytime and Distributed Approaches for Graph Matching

Abu-Aisheh

2016

ELCVIA

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Due to the inherent genericity of graph-based representations, and thanks to the improvement of computer capacities, structural representations have become more and more popular in the field of Pattern Recognition (PR). In a graph-based representation, vertices and their attributes describe objects (or part of them) while edges represent interrelationships between the objects. Representing objects by graphs turns the problem of object comparison into graph matching (GM) where correspondences between vertices and edges of two graphs have to be found [14].In the domain of GM, over the last decade, Graph Edit Distance (GED) has been given a specific attention due to its flexibility to match many types of graphs [2]. GED has been applied to a wide range of specific applications from molecule recognition to image classification [9]. Researchers have shed light on the approximate methods that can find suboptimal solutions hopefully close to the optimal ones but the gap between optimal and suboptimal solutions has not been deeply studied yet.Roughly speaking, two main families of GM have been found in the literature: exact and error-tolerant GM. In this thesis, we propose adding a new GM family, called anytime GM. In order to demonstrate the benefit of having such a family, a new optimized GED algorithm which is based on depth-first search is put forward. This algorithm, referred to as DF, speeds up the computations of GED thanks to its upper and lower bounds' pruning strategy and its preprocessing step. Moreover, DF does not exhaust memory as the number of pending tree search nodes is relatively small thanks to the depth-first search where the number of pending nodes, or so-called partial edit paths, is |V 1 |.|V 2 | in the worst case where |V 1 | and |V 2 | are the numbers of vertices in G 1 and G 2 , respectively. Accordingly, DF outperforms the best-first GED algorithm (A * ) [11] in terms of speed, precision and classification rates. DF is able to provide not only one solution but successive solutions for a better and better quality according to available resources. The anytime version of DF, denoted by ADF, is able to find an initial, possibly suboptimal, solution quickly, keep it in the memory and then continue searching for improved solutions until the convergence to a provably optimal solution. The simplicity of the approach makes it very easy to use; it is also widely applicable. It can be used not only when an optimal solution is desired, but also when we want to see the evolution of the quality of the suboptimal solutions found at each time t. Generally speaking, Anytime GM provides an attractive approach to challenging GM problems, especially when the time Correspondence to: zeina.abu-aisheh@univ-tours.frRecommended for acceptance by David Vázquez Bérmudez

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A large database of graphs and its use for benchmarking graph isomorphism algorithms

Cited by 65 publications

References 9 publications

Portfolios of Subgraph Isomorphism Algorithms

Portfolios of Subgraph Isomorphism Algorithms

Efficient subgraph matching using topological node feature constraints

Anytime and Distributed Approaches for Graph Matching

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