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By Bednorz W.
Bednorz W. Advances in grasping algorithms (In-Teh, 2008)(ISBN 9537619273)(596s)_CsAl_
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It does not deal with the aspects of analyzing and distributing this information, which are application-dependent. If one of the end points of e is in S, let say u ∈ S, then A is only required to include the probe (u, v). 2 22 Advances in Greedy Algorithms 5. Link monitoring We show in this section that for link monitoring both the station selection and probe assignment problems are NP-hard. Then, we present polynomialtime approximation algorithms for solving them. For station selection, we develop a ln(│V│)-approximation algorithm where the lower bound is 1/2· ln(│V│) and for probe assignment, we present a 2 approximation algorithm.
34 Advances in Greedy Algorithms For a graph , we construct the network graph G(V,E) and set of stations S for the probe assignment problem as follows. The graph G contains two root nodes, denoted by r1, r2, and for each node in it contains two additional nodes denoted by wi and ui. The set E of edges of the graph G consists of the following edges. The edge (r1, r2) and for each node in G, the edges (r2,wi) and (wi, ui). Also, for every edge ( , ) in , we add the edge (wi,wj) to G. The weight of each edge (wi,wj) in G is set to 1 + ε, while the remaining edges have a weight of 1.
This is always true as long as the coarsening is achieved in a way that each of the coarsened problems retains the original problem’s global structure. Fig. 2. The Multilevel Generic Algorithm. The key success behind the efficiency of the multilevel techniques is the use of the multilevel paradigm, which offers two main advantages enabling local search techniques to become much more powerful in the multilevel context. First, by allowing local search schemes to view a cluster of vertices as a single entity, the search becomes restricted to only those configurations in the solution space in which the vertices grouped within a cluster are assigned the same label.