Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Acta Informatica
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Journal of the ACM (JACM)
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Nonserial Dynamic Programming
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Discrete Applied Mathematics
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
On global warming: Flow-based soft global constraints
Journal of Heuristics
Integrated Methods for Optimization (International Series in Operations Research & Management Science)
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
MAX ONES Generalized to Larger Domains
SIAM Journal on Computing
Generalizations of the Global Cardinality Constraint for Hierarchical Resources
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Introduction to the Maximum Solution Problem
Complexity of Constraints
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
The complexity of soft constraint satisfaction
Artificial Intelligence
Towards efficient consistency enforcement for global constraints in weighted constraint satisfaction
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
Artificial Intelligence
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Hybrid tractability of valued constraint problems
Artificial Intelligence
Submodularity on a tree: unifying L-convex and bisubmodular functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
On guaranteeing polynomially bounded search tree size
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Hierarchically nested convex VCSP
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Min CSP on four elements: moving beyond submodularity
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A parameterized complexity tutorial
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Modularity-based decompositions for valued CSP
Annals of Mathematics and Artificial Intelligence
Variable elimination in binary CSP via forbidden patterns
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or solving binary Valued Constraint Satisfaction Problems (VCSPs). We study the computational complexity of classes of discrete optimisation problems given by allowing only certain types of costs in every triangle of variable-value assignments to three distinct variables. We show that for several computational problems, the only non-trivial tractable classes are the well known maximum matching problem and the recently discovered joint-winner property. Our results, apart from giving complete classifications in the studied cases, provide guidance in the search for hybrid tractable classes; that is, classes of problems that are not captured by restrictions on the functions (such as submodularity) or the structure of the problem graph (such as bounded treewidth). Furthermore, we introduce a class of problems with convex cardinality functions on cross-free sets of assignments. We prove that while imposing only one of the two conditions renders the problem NP-hard, the conjunction of the two gives rise to a novel tractable class satisfying the cross-free convexity property, which generalises the joint-winner property to problems of unbounded arity.