Tractable constraints on ordered domains
Artificial Intelligence
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Boolean constraint satisfaction: complexity results for optimization problems with arbitrary weights
Theoretical Computer Science
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
The LPSAT Engine & Its Application to Resource Planning
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Tutorial: Complexity of Many-Valued Logics
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Introduction to the Maximum Solution Problem
Complexity of Constraints
Approximability of the Maximum Solution Problem for Certain Families of Algebras
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Bounded tree-width and CSP-related problems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Extensions of the minimum cost homomorphism problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
The maximum solution problem on graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Many combinatorial optimisation problems can be modelled as integer linear programs. We consider a class of generalised integer programs where the constraints are allowed to be taken from a broader set of relations (instead of just being linear inequalities). The set of allowed relations is defined using a many-valued logic and the resulting class of relations have provably strong modelling properties. We give sufficient conditions for when such problems are polynomial-time solvable and we prove that they are APX-hard otherwise.