Integer programming and network flows
The book consists of three parts, linear programming, network flows, and integer programming. Emphasis is placed on the algorithm, its proof, theory and application. Much of the material is new and numerous references are given to cover all aspects of the subject. (Author).
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all-integer arc capacities arc flows artificial variables Assume basic variables basis coefficients column vector components computation consider constraints convex combination convex cone convex hull convex set corresponding cost cut separating cycles cyclic group defined denote disconnecting set distance dual feasible dual program dual simplex method entries equal equation example exists face of P(G feasible solution finite number flow augmenting path Gomory cut group element hyperplane implies INCIDENCE MATRIX inequality integer program Lemma lexicographically linear program max-flow min-cut theorem maximal flow values maximum minimum cut negative nonbasic variables objective function obtained optimum solution pairs of nodes permanent label pivot column pivot row primal feasible primal program problem Proof satisfied shortest chain shortest path shown in Fig simplex method slack variable solve starting tableau subset Theorem tree units of flow VERTICES zero