Integer and combinatorial optimization
Integer and combinatorial optimization
Facets of the three-index assignment polytope
Discrete Applied Mathematics
Linear-time separation algorithms for the three-index assignment polytope
Discrete Applied Mathematics
Polynomial-Time Separation of a Superclass of Simple Comb Inequalities
Mathematics of Operations Research
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Separation algorithms for 0-1 knapsack polytopes
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
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In polyhedral combinatorics, the polytope related to a combinatorial optimization problem is examined in order to obtain families of valid inequalities. To incorporate such families of inequalities within a ‘Branch & Cut' algorithm requires one further step: that of deriving an algorithm which determines whether an inequality of a specific family is violated by a given vector (the separation problem). The idea put forward in this work is to consider a compact representation of the given vector, and measure the complexity of a separation algorithm in terms of this compact representation. We illustrate the idea on the separation of known inequalities for the three index assignment polytope. It turns out that we find new separation algorithms with better complexities than the current ones (that were called best possible).