Feedback vertex sets and cyclically reducible graphs
Journal of the ACM (JACM)
On locating minimum feedback vertex sets
Journal of Computer and System Sciences
A contraction algorithm for finding small cycle cutsets
Journal of Algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
The IceCube approach to the reconciliation of divergent replicas
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
A Polyhedral Approach to the Feedback Vertex Set Problem
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Constant Ratio Approximations of the Weighted Feedback Vertex Set Problem for Undirected Graphs
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
A soft global precedence constraint
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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We consider the problem of finding a cutset in a directed graph G=(V, E), i.e., a set of vertices that cuts all cycles in G. Finding a cutset of minimum cardinality is NP-hard. There exist several approximate and exact algorithms, most of them using graph reduction techniques. In this paper, we propose a constraint programming approach to cutset problems and design a global constraint for computing cutsets. This cutset constraint is a global constraint over boolean variables associated to the vertices of a given graph and states that the subgraph restricted to the vertices having their boolean variable set to true is acyclic. We propose a filtering algorithm based on graph contraction operations and inference of simple boolean constraints, that has a linear time complexity in O(|E| + |V|). We discuss search heuristics based on graph properties provided by the cutset constraint, and show the efficiency of the cutset constraint on benchmarks of the literature for pure minimum cutset problems, and on an application to log-based reconciliation problems where the global cutset constraint is mixed with other boolean constraints.