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A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 285 (15 self)
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A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twentyfive thousand experiments conducted on 100 node random graphs of varying types (graphs with only zeroone links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have...
A performance comparison of five algorithms for graph isomorphism
 in Proceedings of the 3rd IAPR TC15 Workshop on Graphbased Representations in Pattern Recognition
, 2001
"... Despite the significant number of isomorphism algorithms presented in the literature, till now no efforts have been done for characterizing their performance. Consequently, it is not clear how the behavior of those algorithms varies as the type and the size of the graphs to be matched varies in case ..."
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Cited by 34 (2 self)
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Despite the significant number of isomorphism algorithms presented in the literature, till now no efforts have been done for characterizing their performance. Consequently, it is not clear how the behavior of those algorithms varies as the type and the size of the graphs to be matched varies in case of real applications. In this paper we present a benchmarking activity for characterizing the performance of a bunch of algorithms for exact graph isomorphism. To this purpose we use a large database containing 10,000 couples of isomorphic graphs with different topologies (regular graphs, randomly connected graphs, bounded valence graph), enriched with suitably modified versions of them for simulating distortions occurring in real cases. The size of the considered graphs ranges from a few nodes to about 1000 nodes. 1.
A Network Based Approach to Exact and Inexact Graph Matching
, 1993
"... In this paper a new approach to exact and inexact graph matching is introduced. We propose a compact network representation for graphs, which is capable of sharing identical subgraphs of one or several model graphs. The new matching algorithm NA works on the network and uses its compactness in order ..."
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Cited by 4 (0 self)
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In this paper a new approach to exact and inexact graph matching is introduced. We propose a compact network representation for graphs, which is capable of sharing identical subgraphs of one or several model graphs. The new matching algorithm NA works on the network and uses its compactness in order to speed up the detection process. Next, the problem of inexact graph matching is described and a distance measure based on basic graph edit operations and subgraph isomorphism is defined. We propose an inexact network algorithm INA which determines the optimal distance between an input graph and a set of model graphs along with the corresponding subgraph isomorphism. In addition to INA, a new lookahead procedure is proposed. The lookahead procedure works simultaneously over a set of model graphs and efficiently limits the size of the search space. The advantages of the new methods are studied in a theoretical complexity analysis. Finally, some experimental results with randomly generated g...
On the Complexity of Physical Problems and a Swarm Algorithm for kClique Search in Physical Graphs
"... Abstract. As the complexity of systems increases, so does the need of examining the nature of complexity itself. This work discusses the domain of physical swarm problems, in which a swarm of mobile agents is employed for solving physical graph problems (where a certain amount of travel effort in re ..."
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Cited by 2 (2 self)
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Abstract. As the complexity of systems increases, so does the need of examining the nature of complexity itself. This work discusses the domain of physical swarm problems, in which a swarm of mobile agents is employed for solving physical graph problems (where a certain amount of travel effort in required for every movement along the graph’s edges). A new kind of complexity scheme, suitable for this domain, is discussed by examining a central problem of this domain — the physical kclique problem. In this problem, a swarm comprising of mobile agents travels along the vertices of a physical graph G, searching for a clique of size k. Thus, the complexity of the problem is measured in travel efforts (instead of in computation resources). In order to share information between the agents, two communication models are discussed — a complete knowledge sharing (referred to as centralized shared memory) and a distributed shared memory model, where the mobile agents can store and extract information using the graph’s vertices. The work presents a search algorithm for the agents, and discusses its performance under each communication model. The major contribution of this work is demonstrating the strength of the distributed shared memory model. Although this model is much easier to implement and maintain, is highly fault tolerant and has high scalability, the quality of the results it produces is very high, compared to the strongest model of complete knowledge sharing.
Recognition of Shapes By Morphological Attributed Relational Graphs
, 2002
"... Skeletons represent a powerful tool for qualitative shape matching because they resume, synthesize and help the understanding both of the object shape and of its topology. The aim of this work is mainly on using the potential strength of skeleton of discrete objects in computer vision and pattern re ..."
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Skeletons represent a powerful tool for qualitative shape matching because they resume, synthesize and help the understanding both of the object shape and of its topology. The aim of this work is mainly on using the potential strength of skeleton of discrete objects in computer vision and pattern recognition where features of objects are needed for classification. In this paper we propose a method to improve the topological skeleton representation of a binary shape. This allows to find a graph model characterized by efficient and effective attributes, leading to a more correct discrimination between shapes by an attributed graph matching algorithm.
Swarm Intelligence  Cleaners and Hunters
, 2006
"... This work examines the concept of swarm intelligence through three examples of complex problems which are solved by a decentralized swarm of simple agents. The protocols employed by these agents are presented, as well as various analytic results for their performance and for the problems in general. ..."
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This work examines the concept of swarm intelligence through three examples of complex problems which are solved by a decentralized swarm of simple agents. The protocols employed by these agents are presented, as well as various analytic results for their performance and for the problems in general. The problems examined are the problem of finding patterns within physical graphs (e.g. kcliques), the dynamic cooperative cleaners problem, and a problem concerning a swarm of UAVs (unmanned air vehicles), hunting an evading target (or targets). In addition, the work contains a discussion regarding open questions and ongoing and future research in this field.
A Database of Graphs for Isomorphism and SubGraph Isomorphism Benchmarking
"... Despite of the fact that graph based methods are gaining more and more popularity in different scientific areas, it has to be considered that the choice of an appropriate algorithm for a given application is still the most crucial task. The lack of a wide database of graphs make it difficult the tas ..."
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Despite of the fact that graph based methods are gaining more and more popularity in different scientific areas, it has to be considered that the choice of an appropriate algorithm for a given application is still the most crucial task. The lack of a wide database of graphs make it difficult the task of comparing the performances of different graph matching algorithms, and often the selection of an algorithm is made on the basis of a few experimental data available on it. In this paper we describe a database containing 72,800 couples of graphs especially devised for comparing the performance of isomorphism and graphsubgraph isomorphism algorithms. The 72,800 couples are split into 18,200 couples of isomorphic graphs and 54,600 couples of graphs with a subgraph isomorphism mapping among them. The graphs include different categories as Randomly
Parc de Saurupt
, 2006
"... Symbol recognition is a field within graphics recognition to which a lot of efforts have already been devoted. However, a document analysis expert who is more familiar with OCR might rightfully wonder what exactly we call a symbol and how symbol recognition differs from basic character recognition. ..."
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Symbol recognition is a field within graphics recognition to which a lot of efforts have already been devoted. However, a document analysis expert who is more familiar with OCR might rightfully wonder what exactly we call a symbol and how symbol recognition differs from basic character recognition.
1 Hierarchical alignment of weighted directed acyclic graphs
, 2006
"... Abstract — In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the ..."
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Abstract — In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the graphs act as a constraint on the alignment. In this paper, we formalize this problem as the weighted alignment between two directed acyclic graphs. We prove that this problem is NP–complete, prove several upper bounds for approximating the solution, and finally introduce algorithms for several sub–classes of directed acyclic graphs. I. THE PROBLEM Matching or alignment problems are an important set of theoretical problems that appear in many different applications [3], [4], [8]. Depending on the structure of the problem,
Weighted hierarchical alignment of directed acyclic graphs
, 2007
"... Abstract. In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the g ..."
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Abstract. In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the graphs act as a constraint on the alignment. In this paper, we formalize the above problem as the weighted alignment between two directed acyclic graphs. We prove that this problem is NP–complete, show several upper bounds for approximating the solution, and finally introduce polynomial time algorithms for sub–classes of directed acyclic graphs. 1 The problem Matching or alignment problems are an important set of theoretical problems that appear in many different applications [3,4,9]. Depending on the structure of the problem, polynomial time algorithms may or may not exist. In this paper, we propose a new type matching problem called the weighted hierarchical DAG