Advances in Greedy Algorithms by Witold Bednorz

By Witold Bednorz

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20 Advances in Greedy Algorithms propose a scheme for cost-effective placement of monitoring stations for passive monitoring of IP flows and controlling their sampling rate. Recently, Cantieni et al. [23], reformulate the monitoring placement problem. They assume that every node may be a monitoring station at any given time and then they ask the question which monitors should be activated and what should be their sampling to achieve a given measurement task? To this problem they provide optimal solution.

Subsets, as Proof: Let J be a bad SC instance with m elements and constructed in [26] for proving the ln(m) lower bound for the SC problem. Let (J) be the graph calculated by . The lower bound for the PM problem, PM(│V│), satisfies, The number of nodes in the graph (J) is for a large m we assume that │V│  m and thus, PM(│V│) ≥ ln(│V│). 2 A greedy algorithm for station selection Similar to the WLM problem, an efficient solution to a WPM instance is obtained by mapping it to an instance of the CS problem and using the greedy heuristic given in Figure 3 to solve this problem.

10. The RTs of nodes r and u13. 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.

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