## A solution technique for binary integer programming using matchings on graphs |

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### Contents

MATCHINGS ON GRAPHS | 22 |

OBJECTIVE FUNCTION SENSITIVITY ANALYSIS OF OPTIMAL | 65 |

BINARY INTEGER PROGRAMMING ALGORITHM | 88 |

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### Common terms and phrases

ac ac ac uj altering the modified alternating tree binary blossom blossom-weight cyclic coordinate method decrease drug rehabilitation dual objective function dual solution edge i,j edge of G edge-weight endnodes equality subgraph go to Step hungarian tree incidence matrix inner node integer programming ir(i ir(j ir(R Lagrangian relaxation linear programming matching algorithm matching problem modified graph modified section neutral node node-weight for node nodes of G nonlinear programming nonviolating O O UJ objective function value optimal matching original graph outer node packing problem PL/C primal pseudonode root section as shown set packing set partitioning problem shown in Figure shrunk side constraints strong augmenting path subgradient method techniques Theorem transformed back traveling salesman problem tt(R ui uj UJ O UJ uj ui UJ UJ UJ v(LD vector violating nodes weak augmenting path