Generalized polymatroids and submodular flows
Mathematical Programming: Series A and B
An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Logic-based 0-1 constraint programming
Logic-based 0-1 constraint programming
Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Representations of the all_different Predicate of Constraint Satisfaction in Integer Programming
INFORMS Journal on Computing
Constraint and Integer Programming in OPL
INFORMS Journal on Computing
The Role of Integer Programming Techniques in Constraint Programming's Global Constraints
INFORMS Journal on Computing
Neural network-based heuristic algorithms for hypergraph coloring problems with applications
Journal of Parallel and Distributed Computing - Special section best papers from the 2002 international parallel and distributed processing symposium
On the system of two all_different predicates
Information Processing Letters
An Integrated Solver for Optimization Problems
Operations Research
A search-infer-and-relax framework for integrating solution methods
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A polyhedral approach to the alldifferent system
Mathematical Programming: Series A and B
Register allocation via coloring
Computer Languages
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One of the most important logic constraints is the constraint of difference. It is imposed on a set of discrete variables requiring that they receive pairwise distinct values. This construct, initially studied in the field of Artificial Intelligence (in particular, Constraint Programming), has numerous applications and important theoretical properties. In the current work, we show that the polytope associated with this constraint is a generalized polymatroid and thus totally dual integral. As a consequence the problem of optimizing a linear function when variables are restricted to take pairwise distinct values belongs to P. Furthermore, we prove that the above problem can be solved by the greedy algorithm in O(|J| · log|J|) steps where J denotes the set indexing the variables (to receive pairwise distinct values). We establish that the dual of the above problem can also be solved in the same number of steps.