Integer and combinatorial optimization
Integer and combinatorial optimization
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
The vertex set of a 0/1-polytope is strongly P-enumerable
Computational Geometry: Theory and Applications
MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Counting models in integer domains
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
sharpSAT: counting models with advanced component caching and implicit BCP
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Conflict analysis in mixed integer programming
Discrete Optimization
Using Model Counting to Find Optimal Distinguishing Tests
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Exact cover via satisfiability: an empirical study
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
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In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branchand-count paradigm which show the potential of the unrestricted subtree detection.