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Complexity Classification in Infinite-Domain Constraint Satisfaction
  • M. Bodirsky
  • Mathematics, Computer Science
  • ArXiv
  • 4 January 2012
This thesis studies CSPs where the variables can take values from an infinite domain, and studies the limits of complexity classification, and presents classes of computational problems provably do not exhibit a complexity dichotomy into hard and easy problems. Expand
Enumeration and limit laws for series-parallel graphs
It is shown that the number of edges in random series-parallel graphs is asymptotically normal with linear mean and variance, and that it is sharply concentrated around its expected value. Expand
Generating Labeled Planar Graphs Uniformly at Random
An expected polynomial time algorithm is presented to generate a labeled planar graph uniformly at random and recurrence formulas that count all such graphs with n vertices and m edges are derived, based on a decomposition into 1-, 2-, and 3- connected components. Expand
The complexity of temporal constraint satisfaction problems
This work presents 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 language, then the CSP can be solved in polynomial time; otherwise, the C SP is NP-complete. Expand
The complexity of surjective homomorphism problems - a survey
Surjective homomorphism problems seem to be harder to classify and this work examines especially three concrete problems that have arisen from the literature, two of whose complexity remains open. Expand
Well-Nested Drawings as Models of Syntactic Structure ?
This paper investigates drawings (totally ordered forests) as models of syntactic structure. It oers a new model-based perspective on lexicalised Tree Adjoining Grammar by characterising a class ofExpand
Constraint satisfaction with infinite domains
Omega-categoricity is a rather strong model-theoretic assumption on a relational structure, and it can be used to show that many techniques for constraint satisfaction with finite templates extend to omega- categorical templates. Expand
The Complexity of Equality Constraint Languages
This work applies the universal-algebraic approach to infinite-valued constraint satisfaction, and shows that an equality constraint language is tractable if it admits a constant unary polymorphism or an injective binary polymorphism, and is NP-complete otherwise. Expand
Reconstructing the topology of clones
Function clones are sets of functions on a fixed domain that are closed under composition and contain the projections. They carry a natural algebraic structure, provided by the laws of compositionExpand
Constraint Satisfaction with Countable Homogeneous Templates
It is proved that the primitive positive definable relations over an ω-categorical structure Γ are precisely the relations that are preserved by the polymorphisms of Γ. Expand