Integer and combinatorial optimization
Integer and combinatorial optimization
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Reasoning about qualitative temporal information
Artificial Intelligence - Special volume on constraint-based reasoning
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Natural language understanding (2nd ed.)
Natural language understanding (2nd ed.)
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Closure properties of constraints
Journal of the ACM (JACM)
Maintaining reversible DAC for Max-CSP
Artificial Intelligence
Constraint satisfaction over connected row-convex constraints
Artificial Intelligence
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
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Reduction operations in fuzzy or valued constraint satisfaction
Fuzzy Sets and Systems - Optimisation and decision
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Temporal constraint reasoning with preferences
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
The complexity of soft constraint satisfaction
Artificial Intelligence
Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
Communication: Minimum cost homomorphisms to semicomplete multipartite digraphs
Discrete Applied Mathematics
The expressive power of valued constraints: Hierarchies and collapses
Theoretical Computer Science
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
Virtual Arc consistency for weighted CSP
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
The complexity of soft constraint satisfaction
Artificial Intelligence
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Communication: Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
Soft arc consistency revisited
Artificial Intelligence
The expressive power of valued constraints: hierarchies and collapses
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Minimum cost homomorphisms to reflexive digraphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Soft constraints of difference and equality
Journal of Artificial Intelligence Research
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Modularity-based decompositions for valued CSP
Annals of Mathematics and Artificial Intelligence
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Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which associates some measure of desirability with each possible combination of values for those variables. However, the crucial question of the computational complexity of finding the optimal solution to a collection of soft constraints has so far received very little attention. In this paper we identify a class of soft binary constraints for which the problem of finding the optimal solution is tractable. In other words, we show that for any given set of such constraints, there exists a polynomial time algorithm to determine the assignment having the best overall combined measure of desirability. This tractable class includes many commonly-occurring soft constraints, such as "as near as possible" or "as soon as possible after", as well as crisp constraints such as "greater than". Finally, we show that this tractable class is maximal, in the sense that adding any other form of soft binary constraint which is not in the class gives rise to a class of problems which is NP-hard.