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Finding critical independent sets and critical vertex subsets are polynomial problems
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Tractable constraints on ordered domains
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Closure properties of constraints
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Complexity classifications of boolean constraint satisfaction problems
The complexity of maximal constraint languages
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A dichotomy theorem for constraint satisfaction problems on a 3-element set
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A dichotomy for minimum cost graph homomorphisms
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MAX ONES Generalized to Larger Domains
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The complexity of soft constraint satisfaction
Artificial Intelligence
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Generalised integer programming based on logically defined relations
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Tight approximability results for the maximum solution equation problem over Zp
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
An efficient algorithm for a class of constraint satisfaction problems
Operations Research Letters
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Enumerating all solutions of a boolean CSP by non-decreasing weight
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Tractable triangles and cross-free convexity in discrete optimisation
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The complexity of three-element min-sol and conservative min-cost-hom
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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This paper surveys complexity and approximability results for the Maximum Solution (Max Sol ) problem. Max Sol is an optimisation variant of the constraint satisfaction problem. Many important and well-known combinatorial optimisation problems are instances of Max Sol : for example, Max Sol restricted to the domain {0,1} is exactly the Max Ones problem (which, in turn, captures problems such as Independent Set and 0/1 Integer Programming ). By using this relationship, many different problems in logic, graph theory, integer programming, and algebra can be given a uniform treatment. This opens up for new ways of analysing and solving combinatorial optimisation problems.