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320
Symmetry analysis of reversible markov chains
- INTERNET MATHEMATICS
, 2005
"... We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a self-adjoint operator with criteria for an eigenvector to descend to ..."
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Cited by 51 (14 self)
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We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a self-adjoint operator with criteria for an eigenvector to descend to an orbit graph. As examples, we show that the Metropolis construction can dominate a max-degree construction by an arbitrary amount and that, in turn, the fastest mixing Markov chain can dominate the Metropolis construction by an arbitrary amount.
Constraint Satisfaction with Countable Homogeneous Templates
- IN PROCEEDINGS OF CSL’03
, 2003
"... For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that ..."
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Cited by 42 (19 self)
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For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that - as in the case of finite - the computational complexity of CSP( ) for countable homogeneous is determinded by the clone of polymorphisms of . To this end we prove the following theorem which is of independent interest: The primitive positive definable relations over an !-categorical structure are precisely the relations that are invariant under the polymorphisms of .
Datalog and constraint satisfaction with infinite templates
- In Proceedings of the 23rd International Symposium on Theoretical Aspects of Computer Science (STACS’06), LNCS 3884
, 2006
"... Abstract. On finite structures, there is a well-known connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infin ..."
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Cited by 39 (21 self)
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Abstract. On finite structures, there is a well-known connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infinite templates, i.e., for all computational problems that are closed under disjoint unions and whose complement is closed under homomorphisms. If the template Γ is ω-categorical, we obtain alternative characterizations of bounded Datalog width. We also show that CSP(Γ) can be solved in polynomial time if Γ is ω-categorical and the input is restricted to instances of bounded tree-width. Finally, we prove algebraic characterisations of those ω-categorical templates whose CSP has Datalog width (1, k), and for those whose CSP has strict Datalog width k.
The complexity of temporal constraint satisfaction problems
- J. ACM
"... A temporal constraint language is a set of relations that has a first-order definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint langu ..."
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Cited by 33 (22 self)
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A temporal constraint language is a set of relations that has a first-order definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint languages, then the CSP can be solved in polynomial time; otherwise, the CSP is NP-complete. Our proof combines model-theoretic concepts with techniques from universal algebra, and also applies the so-called product Ramsey theorem, which we believe will useful in similar contexts of
Symmetry in Integer Linear Programming
, 2009
"... An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem. Areas where symmetric ILPs arise range from applied settings (scheduling on identical machines), to combinatorics (code construction), and to statistics (statistical designs c ..."
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Cited by 33 (0 self)
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An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem. Areas where symmetric ILPs arise range from applied settings (scheduling on identical machines), to combinatorics (code construction), and to statistics (statistical designs construction). Relatively small symmetric ILPs are extremely difficult to solve using branch-and-cut codes oblivious to the symmetry in the problem. This paper reviews techniques developed to take advantage of the symmetry in an ILP during its solution. It also surveys related topics, such as symmetry detection, polyhedral studies of symmetric ILPs, and enumeration of all non isomorphic optimal solutions.
Tractable symmetry breaking for CSPs with interchangeable values
- IN PROCEEDINGS OF IJCAI’03
, 2003
"... Symmetry breaking in CSPs has attracted considerable attention in recent years. Various general schemes have been proposed to eliminate symmetries during search. In general, these schemes may take exponential space or time to eliminate all symmetries. This paper studies classes of CSPs for which sym ..."
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Cited by 31 (9 self)
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Symmetry breaking in CSPs has attracted considerable attention in recent years. Various general schemes have been proposed to eliminate symmetries during search. In general, these schemes may take exponential space or time to eliminate all symmetries. This paper studies classes of CSPs for which symmetry breaking is tractable. It identifies several CSP classes which feature various forms of value interchangeability and shows that symmetry breaking can be performed in constant time and space during search using dedicated search procedures. Experimental results also show the benefits of symmetry breaking on these CSPs, which encompass many practical applications.
A survey of homogeneous structures
, 2010
"... A relational first order structure is homogeneous if it is countable (possibly finite) and every isomorphism between finite substructures extends to an automorphism. This article is a survey of several aspects of homogeneity, with emphasis on countably infinite homogeneous structures. These arise as ..."
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Cited by 29 (0 self)
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A relational first order structure is homogeneous if it is countable (possibly finite) and every isomorphism between finite substructures extends to an automorphism. This article is a survey of several aspects of homogeneity, with emphasis on countably infinite homogeneous structures. These arise as Fraissé limits of amalgamation classes of finite structures. The subject has connections to model theory, to permutation group theory, to combinatorics (for example through combinatorial enumeration, and through Ramsey theory), to descriptive set theory. Recently there has been a focus on connections to topological dynamics, and to constraint satisfaction. The article discusses connections between these topics, with an emphasis on examples, and on how special properties of an amalgamation class yield consequences for the automorphism group.
The core of a countably categorical structure
- In Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science (STACS’05), LNCS 3404
, 2005
"... Abstract. A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure S has a core, i.e., S has an endomorphism e such that th ..."
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Cited by 25 (19 self)
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Abstract. A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure S has a core, i.e., S has an endomorphism e such that the structure induced by e(S) is a core; moreover, the core is unique up to isomorphism. We prove that every ω-categorical structure has a core. Moreover, every ω-categorical structure is homomorphically equivalent to a model-complete core, which is unique up to isomorphism, and which is finite or ω-categorical. We discuss consequences for constraint satisfaction with ω-categorical templates. 1.
