We describe an algorithm for solving the equicut problem on complete graphs. The core of the algorithm is a cutting-plane procedure that exploits a subset of the linear inequalities defining the convex hull of the incidence vectors of the edge sets that define an equicut. The cuts are generated by several separation procedures that will be described in the paper. Whenever the cutting-plane procedure does not terminate with an optimal solution the algorithm uses a branch-and-cut strategy. We also describe the implementation of the algorithm and the interface with the LP solver. We then report on our computational results.

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Feedback problems consist of removing a minimal number ofvertices of a directed or undirected graph in order to make it acyclic. The problem is known to be NPcomplete. In this paper we consider the variant on undirected graphs. The polyhedral structure of the Feedback V ertex Set polytope is studied. We prove that this polytope is full dimensional and show that some inequalities are facet de ning. We describe a new large class of valid constraints, the subset inequalities. A branch-and-cut algorithm for the exact solution of the problem is then outlined, and separation algorithms for the inequalities studied in the paper are proposed. A Local Search heuristic is described next. Finally we create a library of 1400 random generated instances with the geometric structure suggested by the applications, and we computationally compare the two algorithmic approaches on our library.

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