Optimising the Volgenant–Jonker algorithm for approximating graph edit distance

Jones, William; Chawdhary, Aziem; King, Andy

doi:10.1016/j.patrec.2016.07.024

Cited by 9 publications

(16 citation statements)

References 23 publications

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“…Adaptations of Classical Algorithms LSAPE can also be solved directly by adapting algorithms originally designed for LSAP. An adaptation of the Jonker-Volgenant Algorithm is proposed in [14]. An adaption of the Hungarian Algorithm, denoted HNG in this paper, has been suggested in [4].…”

Section: Cost-constrained Reductions To Lsapmentioning

confidence: 99%

“…Existing LSAPE solvers fall in two categories. Solvers of the first kind reduce LSAPE to LSAP [23,21,27,29,28]: Using different strategies, they first transform an instance C of LSAPE into an instance C of LSAP and then use standard approaches available for LSAP such as the Hungarian Algorithm for computing an optimal solution X for C. Finally, X is transformed into an optimal solution X for the LSAPE instance C. Algorithms of the second kind directly solve LSAPE by adapting existing approaches for LSAP [13,14,4]. Furthermore, LSAPE solvers can be separated in general methods [23,21,13,14,4] and cost-constrained methods that are only applicable to those instances of LSAPE that respect the triangle inequality [27,29,28].…”

Section: Introductionmentioning

confidence: 99%

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Fast linear sum assignment with error-correction and no cost constraints

Bougleux

Gaüzère

Blumenthal

et al. 2020

Pattern Recognition Letters

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We propose an algorithm that efficiently solves the linear sum assignment problem with error-correction and no cost constraints. This problem is encountered for instance in the approximation of the graph edit distance. The fastest currently available solvers for the linear sum assignment problem require the pairwise costs to respect the triangle inequality. Our algorithm is as fast as these algorithms, but manages to drop the cost constraint. The main technical ingredient of our algorithm is a cost-dependent factorization of the node substitutions.

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Section: Cost-constrained Reductions To Lsapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast linear sum assignment with error-correction and no cost constraints

Bougleux

Gaüzère

Blumenthal

et al. 2020

Pattern Recognition Letters

View full text Add to dashboard Cite

show abstract

“…If it is not a square matrix, a column of zeros is added to make it square. Then, we adopt Volgenant-Jonker (VJ) algorithm [32,33] to find a perfect matching in a bipartite graph. Finally, if the vector → p is assigned to center C ( ) , ( ) , = 1 and 0 otherwise.…”

Section: Bbc Algorithm: Balanced Binary Clusteringmentioning

confidence: 99%

Secure and Efficient Image Retrieval over Encrypted Cloud Data

Liang

Zhang

Cheng

et al. 2018

Security and Communication Networks

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This paper proposes a novel image retrieval scheme over encrypted cloud data, which achieves high efficiency and confidentiality. For the purpose of improving search efficiency, an index tree is often deployed in the image retrieval scheme. Meanwhile, the confidentiality of the sensitive cloud data, such as outsourced images, index tree, and query request, is also a key issue. Firstly, a balanced binary clustering algorithm is exploited over the integrated image features composed of basic features, such as HSV histogram and DCT histogram, yielding a balanced binary tree (BBT). In particular, due to the adoption of a balanced index tree, our scheme can achieve logarithmic search time. Secondly, the secure inner product is employed to encrypt the index vector and query feature. Finally, to resist the statistical attack of the frequency distribution of the retrieved results, we copy the database and merge the subtree of encrypted BBT to blind the search results. Security analysis and experimental results show that the proposed scheme is secure and efficient.

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“…Other computational speedups of the Hungarian method are available, which are reported to reduce the execution time in linear assignment problems by up to 90% [36]. Recently, further optimizations of the Jonker and Volgenant algorithm have been reported [37].…”

Section: Computational Complexity Of the Cola Metricmentioning

confidence: 99%

“…The derivation of the COLA metric follows a similar procedure as the OSPA metric [14]. A unique assignment coefficient c i,j = δ j,σ (i) / max{m, m} (38) which satisfies (37), is used where σ(i) is a permutation of the larger set and δ j,σ (i) = 1 iff j = σ(i) and 0 otherwise. Note that if d (c) (m i , m j ) is a metric, then d(m i , m j ) is also guaranteed to be a metric as required in (34).…”

Section: Appendix a Derivation Of The Cola Metricmentioning

confidence: 99%

Metrics for Evaluating Feature-Based Mapping Performance

Barrios

Adams

Leung³

et al. 2017

IEEE Trans. Robot.

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In robotic mapping and simultaneous localization and mapping, the ability to assess the quality of estimated maps is crucial. While concepts exist for quantifying the error in the estimated trajectory of a robot, or a subset of the estimated feature locations, the difference between all current estimated and ground-truth features is rarely considered jointly. In contrast to many current methods, this paper analyzes metrics, which automatically evaluate maps based on their joint detection and description uncertainty. In the tracking literature, the optimal subpattern assignment (OSPA) metric provided a solution to the problem of assessing target tracking algorithms and has recently been applied to the assessment of robotic maps. Despite its advantages over other metrics, the OSPA metric can saturate to a limiting value irrespective of the cardinality errors and it penalizes missed detections and false alarms in an unequal manner. This paper therefore introduces the cardinalized optimal linear assignment (COLA) metric, as a complement to the OSPA metric, for feature map evaluation. Their combination is shown to provide a robust solution for the evaluation of map estimation errors in an intuitive manner. Index Terms-Map metric, simultaneous localization and mapping, mobile robots. I. INTRODUCTION F UNDAMENTAL to any state estimation problem is the concept of estimation error. Solutions to robotic mapping and simultaneous localization and mapping (SLAM), in which usually the location of an unknown number of features should be estimated, are numerous offering various degrees of performance. Examples include classical methods such as recursive EKF SLAM [1], [2], multihypothesis (MH) FastSLAM [3],

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Optimising the Volgenant–Jonker algorithm for approximating graph edit distance

Cited by 9 publications

References 23 publications

Fast linear sum assignment with error-correction and no cost constraints

Fast linear sum assignment with error-correction and no cost constraints

Secure and Efficient Image Retrieval over Encrypted Cloud Data

Metrics for Evaluating Feature-Based Mapping Performance

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