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56
THIRTY YEARS OF GRAPH MATCHING IN PATTERN RECOGNITION
, 2004
"... A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented ..."
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Cited by 137 (1 self)
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A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graphbased techniques in the Pattern Recognition and Machine Vision field.
Symmetry definitions for constraint satisfaction problems
 CONSTRAINTS 11(2–3):115–137
, 2006
"... We review the many different definitions of symmetry for constraint satisfaction problems (CSPs) that have appeared in the literature, and show that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as an operation pr ..."
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Cited by 67 (7 self)
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We review the many different definitions of symmetry for constraint satisfaction problems (CSPs) that have appeared in the literature, and show that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as an operation preserving the constraints. We refer to these as solution symmetries and constraint symmetries. We define a constraint symmetry more precisely as an automorphism of a hypergraph associated with a CSP instance, the microstructure complement. We show that the solution symmetries of a CSP instance can also be obtained as the automorphisms of a related hypergraph, the kary nogood hypergraph and give examples to show that some instances have many more solution symmetries than constraint symmetries. Finally, we discuss the practical implications of these different notions of symmetry.
Solving the Kirkman's Schoolgirl Problem in a Few Seconds
 In Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
, 2002
"... The Social Golfer Problem has been extensively used in recent years by the constraint community as an example of highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right mod ..."
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Cited by 33 (0 self)
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The Social Golfer Problem has been extensively used in recent years by the constraint community as an example of highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as the Kirkman's Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, an generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques allows us to improve previous published results by an order of magnitude for CPU time as well as number of backtracks, and to compute the seven unique solutions of the Kirkman's problem in a few seconds.
Efficient Detection of Network Motifs
 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2006
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Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (Cellular) Algebras
, 1997
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Graphical RuleBased Representation of SignalTransduction Networks
, 2005
"... The process by which a cell senses and responds to its environment, as in signal transduction, is often mediated by a network of proteinprotein interactions, in which proteins combine to form complexes and undergo posttranslational modifications, which regulate their enzymatic and binding activiti ..."
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Cited by 18 (8 self)
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The process by which a cell senses and responds to its environment, as in signal transduction, is often mediated by a network of proteinprotein interactions, in which proteins combine to form complexes and undergo posttranslational modifications, which regulate their enzymatic and binding activities. A typical signaling protein contains multiple sites of protein interaction and modification and may contain catalytic domains. As a result, interactions of signaling proteins have the potential to generate a combinatorially large number of complexes and modified states, and representing signaltransduction networks can be challenging. Representation, in the form of a diagram or model, usually involves a tradeoff between comprehensibility and precision: comprehensible representations tend to be ambiguous or incomplete, whereas precise representations, such as a long list of chemical species and reactions in a network, tend to be incomprehensible. Here, we develop conventions for representing signaltransduction networks that are both comprehensible and precise. Labeled nodes represent components of proteins and their states, and edges represent bonds between components. Binding and enzymatic reactions are described by reaction rules, in which left graphs define the properties of reactants and right graphs define the products that result from transformations of reactants. The reaction rules can be evaluated to derive a mathematical model.
Rulebased modeling of biochemical networks
 Complexity
, 2005
"... We present a method for generating a biochemical reaction network from a description of the interactions of components of biomolecules. The interactions are specified in the form of reaction rules, each of which defines a class of reaction associated with a type of interaction. Reactants within a cl ..."
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Cited by 14 (10 self)
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We present a method for generating a biochemical reaction network from a description of the interactions of components of biomolecules. The interactions are specified in the form of reaction rules, each of which defines a class of reaction associated with a type of interaction. Reactants within a class have shared properties, which are specified in the rule defining the class. A rule also provides a rate law, which governs each reaction in a class, and a template for transforming reactants into products. A set of reaction rules can be applied to a seed set of chemical species and, subsequently, any new species that are found as products of reactions to generate a list of reactions and a list of the chemical species that participate in these reactions, i.e., a reaction network, which can be translated into a mathematical model. © 2005 Wiley Periodicals, Inc. Complexity 10: 22–41, 2005 Key Words: local rules; automatic model generation; networks; signal transduction; combinatorial complexity; systems biology The cell is a complex adaptive system whose emergent behavior we understand only poorly. One reason for our lack of understanding is the complexity of cellular decision making, which is often mediated by a system of interacting proteins. Systems of interacting proteins are particularly prominent in signal transduction [1], 1 the focus Correspondence to: William S. Hlavacek,
Open Babel: An open chemical toolbox
, 2011
"... Background: A frequent problem in computational modeling is the interconversion of chemical structures between different formats. While standard interchange formats exist (for example, Chemical Markup Language) and de facto standards have arisen (for example, SMILES format), the need to interconvert ..."
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Cited by 9 (0 self)
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Background: A frequent problem in computational modeling is the interconversion of chemical structures between different formats. While standard interchange formats exist (for example, Chemical Markup Language) and de facto standards have arisen (for example, SMILES format), the need to interconvert formats is a continuing problem due to the multitude of different application areas for chemistry data, differences in the data stored by different formats (0D versus 3D, for example), and competition between software along with a lack of vendorneutral formats. Results: We discuss, for the first time, Open Babel, an opensource chemical toolbox that speaks the many languages of chemical data. Open Babel version 2.3 interconverts over 110 formats. The need to represent such a wide variety of chemical and molecular data requires a library that implements a wide range of cheminformatics algorithms, from partial charge assignment and aromaticity detection, to bond order perception and canonicalization. We detail the implementation of Open Babel, describe key advances in the 2.3 release, and outline a variety of uses both in terms of software products and scientific research, including applications far beyond simple format interconversion. Conclusions: Open Babel presents a solution to the proliferation of multiple chemical file formats. In addition, it provides a variety of useful utilities from conformer searching and 2D depiction, to filtering, batch conversion, and substructure and similarity searching. For developers, it can be used as a programming library to handle chemical data in areas such as organic chemistry, drug design, materials science, and computational chemistry. It is freely available under an opensource license from
Graph fibrations, graph isomorphism, and PageRank
 RAIRO Inform. Théor
"... Abstract. PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of inneighbourhoods, much in the same way a covering projection is a local isomorphism of neighbour ..."
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Cited by 9 (6 self)
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Abstract. PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of inneighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the values that PageRank can assume. Using our results, we show that a recently defined class of graphs that admit a polynomialtime isomorphism algorithm based on the computation of PageRank is really a subclass of fibrationprime graphs, which possess simple, entirely discrete polynomialtime isomorphism algorithms based on classical techniques for graph isomorphism. We discuss efficiency issues in the implementation of such algorithms for the particular case of web graphs, in which O(n) space occupancy (where n is the number of nodes) may be acceptable, but O(m) is not (where m is the number of arcs).
Automatic configuration recognition methods in modular robots
 International Journal of Robotics Research
, 2008
"... Abstract — Recognizing useful modular robot configurations composed of hundreds of modules is a significant challenge. Matching a new modular robot configuration to a library of known configurations is essential in identifying and applying control schemes. We present three different algorithms to ad ..."
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Cited by 9 (5 self)
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Abstract — Recognizing useful modular robot configurations composed of hundreds of modules is a significant challenge. Matching a new modular robot configuration to a library of known configurations is essential in identifying and applying control schemes. We present three different algorithms to address the problem of (a) matching and (b) mapping new robot configurations onto a library of known configurations. The first method solves the problem using graph isomorphisms and can identify configurations that share the same underlying graph structure, but have different port connections amongst the modules. The second approach compares graph spectra of configuration matrices to find a permutation matrix that maps a given configuration to a known one. The third algorithm exploits the unique structure of the problem for the particular robots used in our research to achieve impressive gains in performance and speed over existing techniques, especially for larger configurations. With these three algorithms, this paper presents novel solutions to the problem of configuration recognition and sheds light on theoretical and practical issues for longterm advances in this important area of modular robotics. Results and examples are provided to compare the performance of the three algorithms and discuss their relative advantages. I.