Assignment Problems

Burkard, Rainer E.; Dell’Amico, Mauro; Martello, Silvano

doi:10.1137/1.9780898717754

Cited by 714 publications

(524 citation statements)

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“…The LSAPE can be efficiently solved in polynomial time complexity by adapting algorithms that initially solve the LSAP. An adaptation of the Hungarian algorithm [5], [16] is presented in [18]. It computes a solution to the LSAPE in O(min{n, m} 2 max{n, m}) time complexity and in O(nm) space complexity.…”

Section: B Problem Formulationmentioning

confidence: 99%

“…This optimization problem is close to the quadratic assignment problem (QAP), see [5] for more details on QAP.…”

Section: B Quadratic Assignment Problem With Edition and Gedmentioning

confidence: 99%

“…While exact solutions to the QAPE could be computed by adapting algorithms that initially solve the QAP [5], this would not be competitive with bipartite GEDs in terms of computational time. So we propose to approximate the GED by adapting the integer projected fixed point (IPFP) algorithm [6], designed to approximate the solution to the QAP, and it is also used in [17] to approximate the GED.…”

Section: Relaxation Approximation Algorithmmentioning

confidence: 99%

“…Under these conditions, the GED can be expressed as a binary quadratic program (QP), which is the subject of this paper. Contrary to the graph matching problem, which can be rewritten as a quadratic assignment problem (QAP) [5], [6], an error-tolerant graph matching can also remove and insert elements. Managing these edit operations is the main difficulty of the quadratic framework.…”

Section: Introductionmentioning

confidence: 99%

“…To approximate the GED, these operations are penalized by the cost of substituting, removing or inserting substructures attached to the nodes [9]- [15]. Since the LSAP can be solved in polynomial time, for instance in O((n + m) 3 ) with the well-known Hungarian algorithm [5], [16], the bGED provides an efficient approximation of the GED. This linear framework has been extended to a quadratic one [17], where the GED is expressed as a global solution of a QAP with (n + m) 2 binary variables.…”

Section: Introductionmentioning

confidence: 99%

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Graph edit distance as a quadratic program

Bougleux

Gaüzère

Brun

2016

2016 23rd International Conference on Pattern Recognition (ICPR)

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Abstract-The graph edit distance (GED) measures the amount of distortion needed to transform a graph into another graph. Such a distance, developed in the context of error-tolerant graph matching, is one of the most flexible tool used in structural pattern recognition. However, the computation of the exact GED is NP-complete. Hence several suboptimal solutions, such as the ones based on bipartite assignments with edition, have been proposed. In this paper we propose a binary quadratic programming problem whose global minimum corresponds to the exact GED. This problem is interpreted as a quadratic assignment problem (QAP) where some constraints on solutions have been relaxed. This allows to adapt the integer projected fixed point algorithm, initially designed for the QAP, to efficiently compute an approximate GED by finding an interesting local minimum. Experiments show that our method remains quite close to the exact GED for datasets composed of small graphs, while keeping low execution times on datasets composed of larger graphs.

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Section: B Problem Formulationmentioning

confidence: 99%

“…This optimization problem is close to the quadratic assignment problem (QAP), see [5] for more details on QAP.…”

Section: B Quadratic Assignment Problem With Edition and Gedmentioning

confidence: 99%

Section: Relaxation Approximation Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Graph edit distance as a quadratic program

Bougleux

Gaüzère

Brun

2016

2016 23rd International Conference on Pattern Recognition (ICPR)

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Combinatorial Traveling Salesman Problem Algorithms

d'Ambrosio

Lodi

Martello

2011

Wiley Encyclopedia of Operations Research and Management Science

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The traveling salesman problem (TSP) is a fundamental and well‐known problem in combinatorial optimization. We start by reviewing some of its ancestors, including the famous Hamiltonian cycle problem of which the TSP is the weighted version. We then introduce the most famous formulations of both the symmetric and the asymmetric TSP, and describe combinatorial approaches for both versions of the problem. We conclude with a brief discussion on the available TSP software.

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UAVSwarms: Decision‐Making Paradigms

Shin

Segui‐Gasco

2014

Encyclopedia of Aerospace Engineering

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The operation of UAV swarms has attracted great attention as their coordination and cooperation could bring significant impact in both military and civilian applications. Despite this potential, there are key challenges to be addressed to enable UAV swarm operations. Unlike operations of a small number of aerial vehicles, the onboard decision‐making responsibility may be more favorably distributed across the UAV swarm taking into account their scalability and sustainability. This chapter addresses three main issues of UAV technologies enabling onboard decision‐making: task allocation, communication network connectivity, and guidance and control in UAV swarm operations. Moreover, state‐of‐the‐art propositions to solve these issues and their limitations are discussed. This chapter also emphasizes the need for a new decision‐making paradigm for more efficient and effective UAV swarm operations and shows its future direction.

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Assignment Problems

Cited by 714 publications

References 0 publications

Graph edit distance as a quadratic program

Graph edit distance as a quadratic program

Combinatorial Traveling Salesman Problem Algorithms

UAVSwarms: Decision‐Making Paradigms

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