The Experts below are selected from a list of 168 Experts worldwide ranked by ideXlab platform

Peter Jeavons - One of the best experts on this subject based on the ideXlab platform.

  • CP - Representing fitness landscapes by valued constraints to understand the complexity of local search
    Lecture Notes in Computer Science, 2019
    Co-Authors: Artem Kaznatcheev, David Cohen, Peter Jeavons
    Abstract:

    Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we introduce a natural approach to modelling fitness landscapes using valued constraints. This allows us to investigate minimal representations (normal forms) and to consider the effects of the structure of the constraint graph on the tractability of local search. First, we show that for fitness landscapes representable by binary Boolean valued constraints there is a minimal necessary constraint graph that can be easily computed. Second, we consider landscapes as equivalent if they allow the same (improving) local search moves; we show that a minimal normal form still exists, but is NP-hard to compute. Next we consider the complexity of local search on fitness landscapes modelled by valued constraints with restricted forms of constraint graph. In the binary Boolean Case, we prove that a tree-structured constraint graph gives a tight quadratic bound on the number of improving moves made by any local search; hence, any landscape that can be represented by such a model will be tractable for local search. We build two families of examples to show that both the conditions in our tractability result are essential. With domain size three, even just a path of binary constraints can model a landscape with an exponentially long sequence of improving moves. With a treewidth two constraint graph, even with a maximum degree of three, binary Boolean constraints can model a landscape with an exponentially long sequence of improving moves.

  • An Algebraic Theory of Complexity for Discrete Optimization
    SIAM Journal on Computing, 2013
    Co-Authors: Davis Cohen, Martin C. Cooper, Peter Jeavons, Paidi Creed, Stanislas Zivny
    Abstract:

    Discrete optimization problems arise in many different areas and are studied under many different names. In many such problems the quantity to be optimized can be expressed as a sum of functions of a restricted form. Here we present a unifying theory of complexity for problems of this kind. We show that the complexity of a finite-domain discrete optimization problem is determined by certain algebraic properties of the objective function, which we call weighted polymorphisms. We define a Galois connection between sets of rational-valued functions and sets of weighted polymorphisms and show how the closed sets of this Galois connection can be characterized. These results provide a new approach to studying the complexity of discrete optimization. We use this approach to identify certain maximal tractable subproblems of the general problem and hence derive a complete classification of complexity for the Boolean Case.

  • the complexity of soft constraint satisfaction
    Artificial Intelligence, 2006
    Co-Authors: David Cohen, Martin C. Cooper, Peter Jeavons, Andrei Krokhin
    Abstract:

    Over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types. One very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations, known as polymorphisms. In this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints. We launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation, which we call a multimorphism. We show that many tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms. We also show that a simple set of NP-hard constraints has very restricted multimorphisms. Finally, we use the notion of multimorphism to give a complete classification of complexity for the Boolean Case which extends several earlier classification results for particular special Cases.

Claudine Chaouiya - One of the best experts on this subject based on the ideXlab platform.

  • Mapping multivalued onto Boolean dynamics
    Journal of Theoretical Biology, 2011
    Co-Authors: Gilles Didier, Elisabeth Remy, Claudine Chaouiya
    Abstract:

    This paper deals with the generalized logical framework defined by René Thomas in the 70's to qualitatively represent the dynamics of regulatory networks. In this formalism, a regulatory network is represented as a graph, where nodes denote regulatory components (basically genes) and edges denote regulations between these components. Discrete variables are associated to regulatory components accounting for their levels of expression. In most Cases, Boolean variables are enough, but some situations may require further values. Despite this fact, the majority of tools dedicated to the analysis of logical models are restricted to the Boolean Case. A formal Boolean mapping of multivalued logical models is a natural way of extending the applicability of these tools. Three decades ago, a multivalued to Boolean variable mapping was proposed by P. Van Ham. Since then, all works related to multivalued logical models and using a Boolean representation rely on this particular mapping. We formally show in this paper that this mapping is actually the sole, up to cosmetic changes, that could preserve the regulatory structures of the underlying graphs as well as their dynamical behaviours.

  • Mapping multivalued onto Boolean dynamics.
    Journal of theoretical biology, 2010
    Co-Authors: Gilles Didier, Elisabeth Remy, Claudine Chaouiya
    Abstract:

    This paper deals with the generalized logical framework defined by Rene Thomas in the 70's to qualitatively represent the dynamics of regulatory networks. In this formalism, a regulatory network is represented as a graph, where nodes denote regulatory components (basically genes) and edges denote regulations between these components. Discrete variables are associated to regulatory components accounting for their levels of expression. In most Cases, Boolean variables are enough, but some situations may require further values. Despite this fact, the majority of tools dedicated to the analysis of logical models are restricted to the Boolean Case. A formal Boolean mapping of multivalued logical models is a natural way of extending the applicability of these tools. Three decades ago, a multivalued to Boolean variable mapping was proposed by P. Van Ham. Since then, all works related to multivalued logical models and using a Boolean representation rely on this particular mapping. We formally show in this paper that this mapping is actually the sole, up to cosmetic changes, that could preserve the regulatory structures of the underlying graphs as well as their dynamical behaviours.

David Cohen - One of the best experts on this subject based on the ideXlab platform.

  • CP - Representing fitness landscapes by valued constraints to understand the complexity of local search
    Lecture Notes in Computer Science, 2019
    Co-Authors: Artem Kaznatcheev, David Cohen, Peter Jeavons
    Abstract:

    Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we introduce a natural approach to modelling fitness landscapes using valued constraints. This allows us to investigate minimal representations (normal forms) and to consider the effects of the structure of the constraint graph on the tractability of local search. First, we show that for fitness landscapes representable by binary Boolean valued constraints there is a minimal necessary constraint graph that can be easily computed. Second, we consider landscapes as equivalent if they allow the same (improving) local search moves; we show that a minimal normal form still exists, but is NP-hard to compute. Next we consider the complexity of local search on fitness landscapes modelled by valued constraints with restricted forms of constraint graph. In the binary Boolean Case, we prove that a tree-structured constraint graph gives a tight quadratic bound on the number of improving moves made by any local search; hence, any landscape that can be represented by such a model will be tractable for local search. We build two families of examples to show that both the conditions in our tractability result are essential. With domain size three, even just a path of binary constraints can model a landscape with an exponentially long sequence of improving moves. With a treewidth two constraint graph, even with a maximum degree of three, binary Boolean constraints can model a landscape with an exponentially long sequence of improving moves.

  • the complexity of soft constraint satisfaction
    Artificial Intelligence, 2006
    Co-Authors: David Cohen, Martin C. Cooper, Peter Jeavons, Andrei Krokhin
    Abstract:

    Over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types. One very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations, known as polymorphisms. In this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints. We launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation, which we call a multimorphism. We show that many tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms. We also show that a simple set of NP-hard constraints has very restricted multimorphisms. Finally, we use the notion of multimorphism to give a complete classification of complexity for the Boolean Case which extends several earlier classification results for particular special Cases.

Gilles Didier - One of the best experts on this subject based on the ideXlab platform.

  • Mapping multivalued onto Boolean dynamics
    Journal of Theoretical Biology, 2011
    Co-Authors: Gilles Didier, Elisabeth Remy, Claudine Chaouiya
    Abstract:

    This paper deals with the generalized logical framework defined by René Thomas in the 70's to qualitatively represent the dynamics of regulatory networks. In this formalism, a regulatory network is represented as a graph, where nodes denote regulatory components (basically genes) and edges denote regulations between these components. Discrete variables are associated to regulatory components accounting for their levels of expression. In most Cases, Boolean variables are enough, but some situations may require further values. Despite this fact, the majority of tools dedicated to the analysis of logical models are restricted to the Boolean Case. A formal Boolean mapping of multivalued logical models is a natural way of extending the applicability of these tools. Three decades ago, a multivalued to Boolean variable mapping was proposed by P. Van Ham. Since then, all works related to multivalued logical models and using a Boolean representation rely on this particular mapping. We formally show in this paper that this mapping is actually the sole, up to cosmetic changes, that could preserve the regulatory structures of the underlying graphs as well as their dynamical behaviours.

  • Mapping multivalued onto Boolean dynamics.
    Journal of theoretical biology, 2010
    Co-Authors: Gilles Didier, Elisabeth Remy, Claudine Chaouiya
    Abstract:

    This paper deals with the generalized logical framework defined by Rene Thomas in the 70's to qualitatively represent the dynamics of regulatory networks. In this formalism, a regulatory network is represented as a graph, where nodes denote regulatory components (basically genes) and edges denote regulations between these components. Discrete variables are associated to regulatory components accounting for their levels of expression. In most Cases, Boolean variables are enough, but some situations may require further values. Despite this fact, the majority of tools dedicated to the analysis of logical models are restricted to the Boolean Case. A formal Boolean mapping of multivalued logical models is a natural way of extending the applicability of these tools. Three decades ago, a multivalued to Boolean variable mapping was proposed by P. Van Ham. Since then, all works related to multivalued logical models and using a Boolean representation rely on this particular mapping. We formally show in this paper that this mapping is actually the sole, up to cosmetic changes, that could preserve the regulatory structures of the underlying graphs as well as their dynamical behaviours.

Artem Kaznatcheev - One of the best experts on this subject based on the ideXlab platform.

  • CP - Representing fitness landscapes by valued constraints to understand the complexity of local search
    Lecture Notes in Computer Science, 2019
    Co-Authors: Artem Kaznatcheev, David Cohen, Peter Jeavons
    Abstract:

    Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we introduce a natural approach to modelling fitness landscapes using valued constraints. This allows us to investigate minimal representations (normal forms) and to consider the effects of the structure of the constraint graph on the tractability of local search. First, we show that for fitness landscapes representable by binary Boolean valued constraints there is a minimal necessary constraint graph that can be easily computed. Second, we consider landscapes as equivalent if they allow the same (improving) local search moves; we show that a minimal normal form still exists, but is NP-hard to compute. Next we consider the complexity of local search on fitness landscapes modelled by valued constraints with restricted forms of constraint graph. In the binary Boolean Case, we prove that a tree-structured constraint graph gives a tight quadratic bound on the number of improving moves made by any local search; hence, any landscape that can be represented by such a model will be tractable for local search. We build two families of examples to show that both the conditions in our tractability result are essential. With domain size three, even just a path of binary constraints can model a landscape with an exponentially long sequence of improving moves. With a treewidth two constraint graph, even with a maximum degree of three, binary Boolean constraints can model a landscape with an exponentially long sequence of improving moves.