A linear programming approach for the weighted graph matching problem

Almohamad, H.A.; Duffuaa, Salih O.

doi:10.1109/34.211474

Cited by 196 publications

(153 citation statements)

References 3 publications

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“…The quadratic assignment problem, however, is NP-hard [13], and suboptimal solutions are achieved by means of various relaxations. Approaches are either purely discrete [14], [15] or continuous [16], based on the solution of differential equations that always converge to a discrete assignment.…”

Section: R Ecent Advances In Communication and Computationmentioning

confidence: 99%

Dynamic Assignment in Distributed Motion Planning with Limited Information

Zavlanos

Pappas

2007

2007 American Control Conference

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Abstract-Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dynamically assign targets or destinations to multiple homogeneous agents, not relying on any a priori assignment of agents to destinations. In this paper, we address this challenge using two novel ideas. First, distributed multidestination potential fields are developed that are able to drive every agent to any available destination. Second, nearest neighbor coordination protocols are developed ensuring that distinct agents are assigned to distinct destinations. Integration of the overall system results in a distributed, multiagent, hybrid system for which we show that the mutual exclusion property of the final assignment is guaranteed for almost all initial conditions. Furthermore, we show that our dynamic assignment algorithm will converge after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.Index Terms-Distributed control, hybrid systems, motion planning, multiagent assignment problems.

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Section: R Ecent Advances In Communication and Computationmentioning

confidence: 99%

Dynamic Assignment in Distributed Motion Planning with Limited Information

Zavlanos

Pappas

2007

2007 American Control Conference

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“…However, graph matching is a difficult problem in itself. Whenever the two graphs to be matched have the same number of nodes, graph matching is equivalent to searching for graph isomorphism and polynomial time solutions exist in this case, [14], [15], [16]. It is however rarely the case that the image graph have the same size as the object graph: The problem is therefore equivalent to maximum subgraph matching -find the largest isomorphic subgraphs of the two graphs.…”

Section: Introductionmentioning

confidence: 99%

Polyhedral object recognition by indexing

Horaud¹,

Sossa²

1995

Pattern Recognition

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“…Except for some earlier approaches not suited to sub-graph matching, such as [8][9][10], most optimization-based algorithms require the explicit calculation of compatibility values between vertices and edges, either using compatibility functions or probability distributions. In addition, some Bayesian-based approaches fail when graphs are fully connected [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In general, the first approach constructs a state-space, which is searched using heuristics to reduce complexity [2][3][4][5][6][7]. The second approach, which is the one adopted here, is based on function optimization techniques which include Bayesian, linear-programming, continuation, eigen-decomposition, polynomial transform, genetic, neural network and relaxation-based methods [1,[8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Non-bayesian Graph Matching without Explicit Compatibility Calculations

Wyk

2002

Lecture Notes in Computer Science

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Abstract. This paper introduces a novel algorithm for performing Attributed Graph Matching (AGM). A salient characteristic of the Interpolator-Based Kronecker Product Graph Matching (IBKPGM) algorithm is that it does not require the explicit calculation of compatibility values between vertices and edges, either using compatibility functions or probability distributions. No assumption is made about the adjacency structure of the graphs to be matched. The IBKPGM algorithm uses Reproducing Kernel Hilbert Space (RKHS) interpolator theory to obtain an unconstrained estimate to the Kronecker Match Matrix (KMM) from which a permutation sub-matrix is inferred.

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A linear programming approach for the weighted graph matching problem

Abstract: Abstract-One is based on an eigendecomposition approach and the other on a symmetric polynomial transform. Experimental results showed that the LP approach is superior in matching graphs than both other methods.

Cited by 196 publications

References 3 publications

Dynamic Assignment in Distributed Motion Planning with Limited Information

Dynamic Assignment in Distributed Motion Planning with Limited Information

Polyhedral object recognition by indexing

Non-bayesian Graph Matching without Explicit Compatibility Calculations

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