Cisco - Catalyst 6000 Product Update 1104

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LDAP System Administration

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Additional resources for Cisco - Catalyst 6000 Product Update 1104

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0, 3. 2_>ru>_ 1 a n d 2 > r v _ > 1. A characteristic of these decompositions is that the subproblems must be solved in a certain order, not independently of each other, since the output of several of these subproblems determines the input to the last one. Both Nodes in t h e A r t i c u l a t i o n Set Are of Type 0 Consider a k E C O N problem, given by a graph G = (V, E) and a node type vector r E ~ v . ) Let { u , v } be an articulation set with ru = rv = 0, such that G - {u,v} has two components G1 = (V1,/)I) and G2 = (1)2,/)2) with v ( G ) = 1 and r(V2) >_ 1.

5: Gadget 40 No C H A P T E R 4. D E C O M P O S I T I O N Node in the Articulation Set Is of Type 0 If both nodes u and v in the articulation set are of type 1 or 2, we need only distinguish between partial solutions of type (a) or (d), so we only compute the values a and d and solve the kECON problem on the graph G2 with an additional uv-edge of cost d - a. The additive constant z is a. ) If the edge uv is used by an optimal solution C, we replace uv in C by the optimal partial tree of type (d), otherwise we augment C by the optimal partial tree of type (a).

If there exist edges uv, we add t h e m either to G1 or to G2 but not to both. If C C_ E is a feasible solution to the kECON problem on G, the set T := C C~E1 (called a "partial tree") may have four different forms, according to whether u and v are connected in T, or whether u or v are used at all. More exactly, T is a feasible solution to one of the four following Steiner tree problems (P~), (Pb), (Pc), (Pd). These subproblems are defined on G1 and use the same costs and the same node types for all nodes in V~ \ {u,v} as in the original problem; only the node types of u and v vary as follows: (P~): r~ = 1 and rv = 1 and an artificial edge uv with cost 0 is added; (Pb): r~ = 0 and r~ = 1; (P~): r~ = 1 and r~ = O; (Pd): r~ = 1 and r~ = 1.

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