Bauer P.'s A branch and cut approach to the cardinality constrained PDF

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Fig. 1. An embedding of C and PeT Now, suppose for a contradiction that the coefficient for edge f ∈ E \ T cannot be increased to wlTf , this implies by Lemma 2 that 2 − l Tf + 2 − z f ≤ wlTf − 1. 1) Since edge f must be in an optimal solution x to problem (CIP), we have zf = x e + 2 − l Tf + e∈T we x e . 2) gives that wlTf + we x e ≥ 3 − e∈(E\T )\ f xe. 3) e∈T Let C be the optimal circuit defined by incidence vector x. Define m as m ≡ |C ∩ (E \ T )|. We now proceed to prove the validity of the coefficient improvements on a case by case basis.

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A branch and cut approach to the cardinality constrained circuit problem by Bauer P.


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