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

By Bauer P.

Show description

Read or Download A branch and cut approach to the cardinality constrained circuit problem PDF

Best genetics books

Molecular Genetics of Recombination

This paintings bargains a desirable perception right into a an important genetic strategy. Recombination is, comfortably, probably the most vital issues in modern biology. This publication is a wholly entire therapy of the topic, summarizing all current perspectives at the subject and whilst placing them into context.

Zugang zu humangenetischen Ressourcen indigener Völker Lateinamerikas: Eine Stakeholderanalyse

María Cristina Blohm untersucht die Problematik des Zugangs und der Nutzung humangenetischer Ressourcen Indigener Lateinamerikas und stellt auf der foundation des Stakeholderansatzes Lösungsansätze vor, welche die fundamentale Grundrechte und Grundfreiheiten des Menschen sowie die bioethischen Grundprinzipien für populationsbezogene Forschungsorganisationen berücksichtigen.

Extra info for A branch and cut approach to the cardinality constrained circuit problem

Sample text

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.

K is odd, l Tf = 3k/2 +2i for some i ∈ such that l gT ≥ k. + , and ∃g ∈ C ∩(E \ T \ f ) 342 P. Bauer et al. In this subcase, we know that wlTf = (5−k)/2 and we = 2−leT ∀e ∈ (C\ f )∩(E\T ). 3) implies that (2 − leT ) ≥ 3 − (5 − k)/2 + e∈(C\ f )∩(E\T ) Using the fact that e∈T xe. 16) and applying Lemma 3, we get that |P Tf ∩ C| − |PeT \ P Tf | ≥ k − m + 3. e∈(C\ f )∩(E\T ) Therefore, |C| ≥ |P Tf ∩ C| + m ≥ k + 3 + |PeT \ P Tf | ≥ k + 3, e∈E\T \ f which gives the contradiction |C| > k. We have shown that in all possible cases, if the coefficient of an edge e ∈ E \ T in the original tree inequality cannot be improved to wlTe , then there is a contradiction.

1986): Clique tree inequalities and the symmetric travelling salesman problem. Mathematics of Operations Research 11, 537–569 20. Gusfield, D. (1990): Very simple methods for all pairs network flow analysis. SIAM Journal of Computing 19, 143–155 21. , Ozluk, O. (1998): Facets of the p-cycle polytope. Technical Report UNC/OR TR98-1, Department of Operations Research, University of North Carolina 22. C. (1974): Optimum communication spanning trees. SIAM Journal on Computing 3, 188–195 23. L. (1973): Graph partitioning and constructing optimal decision trees and polynomial complete problems.

Download PDF sample

Rated 4.06 of 5 – based on 3 votes