Network Flows: Theory, Algorithms, and ApplicationsA comprehensive introduction to network flows that brings together the classic and the contemporary aspects of the field, and provides an integrative view of theory, algorithms, and applications.
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Page 607
... Lagrangian Relaxation and Inequality Constraints In the optimization model ( P ) , the constraints Ax = b are all equality constraints . In practice , we often encounter models , such as the constrained ... Lagrangian Relaxation Technique.
... Lagrangian Relaxation and Inequality Constraints In the optimization model ( P ) , the constraints Ax = b are all equality constraints . In practice , we often encounter models , such as the constrained ... Lagrangian Relaxation Technique.
Page 620
... Lagrangian subproblem of the optimization problem ( P ) satisfies the integrality property , then z ° = L * . Proof . Observe that the problem min { dx ... Lagrangian Relaxation and Network Optimization Applications of Lagrangian Relaxation,
... Lagrangian subproblem of the optimization problem ( P ) satisfies the integrality property , then z ° = L * . Proof . Observe that the problem min { dx ... Lagrangian Relaxation and Network Optimization Applications of Lagrangian Relaxation,
Page 637
... Lagrangian relaxation as a conceptual as well as algorithmic tool . On some occasions , as in our discussion of the degree - constrained minimum span- ning tree problem , we can use the bounding information provided by Lagran- gian ...
... Lagrangian relaxation as a conceptual as well as algorithmic tool . On some occasions , as in our discussion of the degree - constrained minimum span- ning tree problem , we can use the bounding information provided by Lagran- gian ...
Contents
INTRODUCTION | 1 |
PATHS TREES AND CYCLES | 23 |
ALGORITHM DESIGN AND ANALYSIS | 53 |
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adjacency list Application arc costs arc flows arc lengths augmenting path augmenting path algorithm bipartite capacity scaling algorithm commodity constraints cost flow problem define denote Dijkstra's algorithm directed path discussion distance label example Exercise feasible flow feasible solution Fibonacci heap flow algorithms formulation implementation integer iteration label-correcting algorithm Lagrangian multiplier Lagrangian relaxation Lemma linear programming lower bound matching matrix maximum flow problem minimum cost flow minimum spanning tree multicommodity flow problem N₁ negative cycle network contains network flow problem network G network simplex algorithm node potentials nonnegative NP-complete O(nm objective function value operation optimal solution optimality conditions path from node polynomial preflow-push algorithm reduced cost residual network s-t cut satisfies scaling phase Section shortest path distances shortest path problem Show shown in Figure simplex method source node Suppose Theorem undirected units of flow upper bound variables zero