Linear Assignment Problems and Extensions

Burkard, Rainer E.; Çela, Eranda

doi:10.1007/978-1-4757-3023-4_2

Cited by 247 publications

(149 citation statements)

References 152 publications

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“…. , n that minimises n i=0 C i,p i (Munkres, 1957;Burkard and Cela, 1999). Any algorithm capable of finding an optimal solution to the assignment problem, such as the Hungarian algorithm (Kuhn, 1955), can be used in the derivation of a (suboptimal) solution to the GED problem (Riesen et al, 2007).…”

Section: The Linear Assignment Problem and Gedmentioning

confidence: 99%

Optimising the Volgenant–Jonker algorithm for approximating graph edit distance

Jones

Chawdhary

King

2017

Pattern Recognition Letters

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Although it is agreed that the Volgenant-Jonker (VJ) algorithm provides a fast way to approximate graph edit distance (GED), until now nobody has reported how the VJ algorithm can be tuned for this task. To this end, we revisit VJ and propose a series of refinements that improve both the speed and memory footprint without sacrificing accuracy in the GED approximation. We quantify the effectiveness of these optimisations by measuring distortion between control-flow graphs: a problem that arises in malware matching. We also document an unexpected behavioural property of VJ in which the time required to find shortest paths to unassigned vertices decreases as graph size increases, and explain how this phenomenon relates to the birthday paradox.

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Section: The Linear Assignment Problem and Gedmentioning

confidence: 99%

Optimising the Volgenant–Jonker algorithm for approximating graph edit distance

Jones

Chawdhary

King

2017

Pattern Recognition Letters

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“…This problem is called linear bottleneck assignment (LBAP) [8] and can be solved optimally by any of the polynomial-time algorithms based on network flow theory [9].…”

Section: B Partition Strategymentioning

confidence: 99%

Scalable and Practical Pursuit-Evasion

Vieira¹,

Govindan²,

Sukhatme³

2009

Proceedings of the 2nd International Conference on Robotic Communication and Coordination

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Abstract-In this paper, we consider the design and implementation of practical, yet near-optimal, pursuit-evasion games. In prior work, we developed, using the theory of zero-sum games, minimal completion-time strategies for pursuit-evasion. Unfortunately, those strategies do not scale beyond a small number of robots. In this paper, we design and implement a partition strategy where pursuers capture evaders by decomposing the game into multiple multi-pursuer single-evader games. Our algorithm terminates, has bounded capture time, is robust, and is scalable in the number of robots. In our implementation, a sensor network provides sensing-at-a-distance, as well as a communication backbone that enables tighter coordination between pursuers. Our experiments in a challenging office environment suggest that this approach is near-optimal, at least for the configurations we have evaluated. Overall, our work illustrates an innovative interplay between robotics and communication.

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“…However, the large scale problem can be time-consuming in order to solve for the optimal solution. Algorithms for solving LAP can be divided into six groups; primal-dual, simplex-based, primal (non-simplex), dual simplexbased, dual (non-simplex) algorithms and parallel algorithms (Burkard and Cela, 1999). Sixty years ago, Harold H. Kuhn proposed a primaldual algorithm as the Hungarian method, the first polynomial-time method for the assignment problem, can solve the real world problem easily.…”

Section: Introductionmentioning

confidence: 99%

“…The pseudo-flow algorithm applies ε-complementary conditions whereas the auction algorithm applies cost scaling. The family of pseudo-flow algorithms were developed by J.B.Orlin and R.K.Ahuja in 1987, A.V.Goldberg, S.A.Plotkin and P.Vaidya in 1993, A.V.Goldberg and R.Kennedy in 1995 (Burkard et al, 2009 (Burkard and Cela, 1999). However, the format of FORTRAN and PASCAL language are inefficient for constructing a large scale cost matrix.…”

Section: Introductionmentioning

confidence: 99%

A Successive Admissible Cell Method for Solving Large Scale Linear Assignment Problem with Dense Cost Matrix

Boonphakdee¹,

Charnsethikul²

2016

Journal of Computer Science

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Normally, the Linear Assignment Problem (LAP) has been solved by successful algorithms such as Lapjv and Munkres programmed as MATLAB codes. This study presented an improved algorithm for solving large scale LAP. A preprocessing (PP) algorithm was proposed to apply for constructing the k th transferred reduced cost matrix then this matrix was solved by Lapjvalgorithm. Performances of PP-Lapjvalgorithm were faster than theoriginal Lapjv about 1.90-8.20% when problem sizes are expanded from problem sizes 18000 to 34000 on integer number range [1,10] and [1,1000]. On the other hand, PP-Lapjvalgorithm was inefficient on integer number range [1, 1000000] due to more timeconsuming for executing Lapjv.m file in PP-Lapjvalgorithm. The enlargement of number ranges is influenced to the average computation time of Lapjvalgorithm raised about 53.63% and 32.05% when the range is expanded from [1,1000] to [1,1000000] on problem sizes 18000 and 30000,respectively. The limitations of problem size were determined by virtual memory of the tested computer that both algorithms enabled to solve at the maximum problem size of 34000.

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Linear Assignment Problems and Extensions

Cited by 247 publications

References 152 publications

Optimising the Volgenant–Jonker algorithm for approximating graph edit distance

Optimising the Volgenant–Jonker algorithm for approximating graph edit distance

Scalable and Practical Pursuit-Evasion

A Successive Admissible Cell Method for Solving Large Scale Linear Assignment Problem with Dense Cost Matrix

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