A new polynomial-time algorithm for linear programming
Combinatorica
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Tractable constraints on ordered domains
Artificial Intelligence
The essence of constraint propagation
Theoretical Computer Science
Realization of set functions as cut functions of graphs and hypergraphs
Discrete Mathematics
Radio Link Frequency Assignment
Constraints
New Lower Bounds of Constraint Violations for Over-Constrained Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Discrete Applied Mathematics
Reduction operations in fuzzy or valued constraint satisfaction
Fuzzy Sets and Systems - Optimisation and decision
Arc consistency for soft constraints
Artificial Intelligence
Cyclic consistency: a local reduction operation for binary valued constraints
Artificial Intelligence
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
A faster strongly polynomial time algorithm for submodular function minimization
Mathematical Programming: Series A and B
Hybrid tractable CSPs which generalize tree structure
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Exploiting tree decomposition and soft local consistency in weighted CSP
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
In the quest of the best form of local consistency for weighted CSP
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Bounds arc consistency for weighted CSPs
Journal of Artificial Intelligence Research
Refining the basic constraint propagation algorithm
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Temporal constraint reasoning with preferences
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Existential arc consistency: getting closer to full arc consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
The complexity of soft constraint satisfaction
Artificial Intelligence
Reasoning from last conflict(s) in constraint programming
Artificial Intelligence
Russian Doll search with tree decomposition
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
MiniMaxSAT: a new weighted Max-SAT solver
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Exact solution of permuted submodular minsum problems
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
The partial constraint satisfaction problem: Facets and lifting theorems
Operations Research Letters
Expert Systems with Applications: An International Journal
DR.FILL: crosswords and an implemented solver for singly weighted CSPs
Journal of Artificial Intelligence Research
Read-once resolution for unsatisfiability-based Max-SAT algorithms
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Minimum satisfiability and its applications
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Pairwise decomposition for combinatorial optimization in graphical models
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Managing dynamic CSPs with preferences
Applied Intelligence
Journal of Artificial Intelligence Research
Consistencies for ultra-weak solutions in minimax weighted CSPs using the duality principle
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Propagating soft table constraints
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
WCSP integration of soft neighborhood substitutability
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
A new encoding from MinSAT into MaxSAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Computational protein design as a cost function network optimization problem
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Dynamic virtual arc consistency
Proceedings of the 28th Annual ACM Symposium on Applied Computing
Modularity-based decompositions for valued CSP
Annals of Mathematics and Artificial Intelligence
The power of linear programming for finite-valued CSPs: a constructive characterization
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The Valued Constraint Satisfaction Problem (VCSP) is a generic optimization problem defined by a network of local cost functions defined over discrete variables. It has applications in Artificial Intelligence, Operations Research, Bioinformatics and has been used to tackle optimization problems in other graphical models (including discrete Markov Random Fields and Bayesian Networks). The incremental lower bounds produced by local consistency filtering are used for pruning inside Branch and Bound search. In this paper, we extend the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously. Over the rationals and allowing simultaneous operations, we show that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming. This defines Optimal Soft Arc Consistency (OSAC). To reach a more practical algorithm, we show that the existence of a sequence of arc consistency operations which increases the lower bound can be detected by establishing arc consistency in a classical Constraint Satisfaction Problem (CSP) derived from the original cost function network. This leads to a new soft arc consistency method, called, Virtual Arc Consistency which produces improved lower bounds compared with previous techniques and which can solve submodular cost functions. These algorithms have been implemented and evaluated on a variety of problems, including two difficult frequency assignment problems which are solved to optimality for the first time. Our implementation is available in the open source toulbar2 platform.