By Bednorz W.

Bednorz W. Advances in grasping algorithms (In-Teh, 2008)(ISBN 9537619273)(596s)_CsAl_

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Further, the experimental results demonstrate the effectiveness of the presented algorithms for accurately monitoring large networks with very few monitoring stations and probe messages close to the number of network links. 9. References [1] William Stallings. “SNMP, SNMPv2, SNMPv3, and RMON 1 and 2”. , 1999. (Third Edition). [2] “NetFlow Services and Applications”. Cisco Systems White Paper, 1999. [3] S. R. Stevens, “TCP/IP illustrated”, Addison-Wesley Publishing Company, 1994. [4] Cooperative Association for Internet Data Analysis (CAIDA).

2 An efficient station selection algorithm The station selection problem for path monitoring is defined as follows. Definition 3 (The Weighted Path Monitoring Problem - WPM): Given a graph G(V,E), with a weight wv and a RT Tv for every node v ∈ V , and a routing path Pu,v between any pair of 30 Advances in Greedy Algorithms nodes u, v ∈ V , find the set S ⊆ V that minimizes the sum Σv∈S wv such that for every pair u, □ v ∈ V there is a station s ∈ S such that Pu,v ⊆ Ts. In the un-weighted version of the WPM problem, termed the path monitoring (PM) problem, the weight of every node is 1.

In our lower bound proof, we use a polynomial reduction, , from any instance I(Z,Q) of the SC problem to a corresponding PM instance. The graph (V,E) computed by the reduction contains the following nodes. The nodes ui and sj for every element zi ∈ Z and set Qj ∈ Q, respectively, and three additional nodes u0, t and r. The node u0 corresponds to a dummy element z0 that is included in every set Qj ∈ Q, and each one of the nodes t and r is the hub of a star that is connected to the rest of the nodes.