Theory of linear and integer programming
Theory of linear and integer programming
Handbook of combinatorics (vol. 2)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
0/1-Integer Programming: Optimization and Augmentation are Equivalent
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A primal branch-and-cut algorithm for the degree-constrained minimum spanning tree problem
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
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The 0/1 primal separation problem is: Given an extreme point x of a 0/1 polytope P and some point x*, find an inequality which is tight at x, violated by x* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent.We apply this result to the perfect matching problem. Here, primal separation is easier than its standard version. We present an algorithm for primal separation, which rests only on simple max-flow computations. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. In contrast, the known standard separation method involves Padberg and Rao's minimum odd cut algorithm, which itself is based on the construction of a Gomory-Hu tree.