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13
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 .
Constraint Satisfaction Problems with Countable Homogeneous Templates
"... Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a nonuniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ωcategorical. We survey examples of such problems in ..."
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Cited by 25 (10 self)
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Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a nonuniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ωcategorical. We survey examples of such problems in temporal and spatial reasoning, infinitedimensional algebra, acyclic colorings in graph theory, artificial intelligence, phylogenetic reconstruction in computational biology, and tree descriptions in computational linguistics. We then give an introduction to the universalalgebraic approach to infinitedomain constraint satisfaction, and discuss how cores, polymorphism clones, and pseudovarieties can be used to study the computational complexity of CSPs with ωcategorical templates. The theoretical results will be illustrated by examples from the mentioned application areas. We close with a series of open problems and promising directions of future research.
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 ωcategorical structure has a core. Moreover, every ωcategorical structure is homomorphically equivalent to a modelcomplete core, which is unique up to isomorphism, and which is finite or ωcategorical. We discuss consequences for constraint satisfaction with ωcategorical templates. 1.
A New Algorithm for Normal Dominance Constraints
 In Proc. SODA
, 2003
"... this paper, we propose a novel graph algorithm relying on graph connectivity, and inspired by [3]. It can enumerate all solved forms of a normal dominance constraint 2 ) per solved form, and thereby improves on the best previously known algorithm in e#ciency. # Humboldt Universitat zu Berlin, Germa ..."
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Cited by 16 (5 self)
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this paper, we propose a novel graph algorithm relying on graph connectivity, and inspired by [3]. It can enumerate all solved forms of a normal dominance constraint 2 ) per solved form, and thereby improves on the best previously known algorithm in e#ciency. # Humboldt Universitat zu Berlin, Germany + LORIA, Nancy, France # INRIA team Mostrare, Universite de Lille, France Universitat des Saarlandes, Germany Subquadratic running time can be achieved employing decremental graph biconnectivity algorithms
An Efficient Algorithm for Weakly Normal Dominance Constraints
 In ACMSIAM Symposium on Discrete Algorithms
, 2004
"... Dominance constraints are logical descriptions of trees. E cient algorithms for the subclass of normal dominance constraints were proposed recently. We present a new and simpler graph algorithm which solves more expressive weakly normal dominance constraints. We thereby improve on the best prev ..."
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Cited by 12 (1 self)
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Dominance constraints are logical descriptions of trees. E cient algorithms for the subclass of normal dominance constraints were proposed recently. We present a new and simpler graph algorithm which solves more expressive weakly normal dominance constraints. We thereby improve on the best previously known algorithm for normal dominance constraints in eciency, coverage, and applicability.
Determining the consistency of partial tree descriptions
 Artificial Intelligence
"... Abstract. We present an efficient algorithm that decides the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in ..."
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Cited by 8 (6 self)
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Abstract. We present an efficient algorithm that decides the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in an ordered tree. Cornell asked for an algorithm to find a tree structure satisfying these constraints. This computational problem generalizes the commonsupertree problem studied in phylogenetic analysis, and also generalizes the network consistency problem of the socalled leftlinear point algebra. We present the first polynomial time algorithm for Cornell’s problem, which runs in time O(mn), where m is the number of constraints and n the number of variables in the constraint.
Understanding Aspects through Call Graph Enumeration and Pointcut Satisfiability
"... Abstract. An aspectoriented program can be split into an aspect program and a target program to which these aspects are applied. The aspect program contains pointcuts that select interesting points in the target program. In an effort to componentize and better understand these aspects, we would lik ..."
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Abstract. An aspectoriented program can be split into an aspect program and a target program to which these aspects are applied. The aspect program contains pointcuts that select interesting points in the target program. In an effort to componentize and better understand these aspects, we would like to reason about them in the absense of target programs. As a first step we present an algorithm that builds a representation of the set of call graphs to which a pointcut can apply – a problem called call graph enumeration. We also decide whether this set is nonempty – a problem called pointcut satisfiability. Solutions to these problems may help to componentize and assign useful types to aspectoriented programs. 1
Determining the Consistency of Partial Tree Descriptions
 ARTIFICIAL INTELLIGENCE
, 2007
"... We present an efficient algorithm that checks the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in an ord ..."
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We present an efficient algorithm that checks the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in an ordered tree. Cornell asked for an algorithm to find a tree structure satisfying these constraints. This computational problem generalizes the commonsupertree problem studied in phylogenetic analysis. We present the first polynomial time algorithm for Cornell's problem, which runs in time O(mn), where m is the number of constraints and n the number of variables in the constraint.
Satisfiability of XPath Expressions
"... In this paper, we investigate the complexity of deciding the satisfiability of XPath 2.0 expressions, i.e., whether there is an XML document for which their result is nonempty. Several fragments that allow certain types of expressions are classified as either in PTIME or NPhard to see which type of ..."
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In this paper, we investigate the complexity of deciding the satisfiability of XPath 2.0 expressions, i.e., whether there is an XML document for which their result is nonempty. Several fragments that allow certain types of expressions are classified as either in PTIME or NPhard to see which type of expression make this a hard problem. Finally, we establish a link between XPath expressions and partial tree descriptions which are studied in computational linguistics. 1
Combining Tree Partitioning, Precedence,
"... Abstract. The tree and path constraints, for digraph partitioning by vertexdisjoint trees and paths respectively, are unified within a single global constraint, including a uniform treatment of a variety of useful side constraints, namely precedence, incomparability, and degree constraints. The key ..."
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Abstract. The tree and path constraints, for digraph partitioning by vertexdisjoint trees and paths respectively, are unified within a single global constraint, including a uniform treatment of a variety of useful side constraints, namely precedence, incomparability, and degree constraints. The key point of the filtering is to take partially into account the strong interactions between the tree partitioning problem and all the side constraints, in order to avoid thrashing during search. Finally, our approach is evaluated on three applications: the Hamiltonian path problem, the ordered disjoint path problem, and the phylogenetic supertree problem. 1