Advances in Greedy Algorithms by Witold Bednorz

By Witold Bednorz

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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. 3. Network model We model the Service Provider or Enterprise IP network by an undirected graph G(V,E), where the graph nodes, V, denote the network routers and the edges, E, represent the communication links connecting them. The number of nodes and edges is denoted by ā”‚Vā”‚ and ā”‚Eā”‚, respectively.

Another widely used variant of GSAT is the WalkSAT algorithm originally introduced in [12]. It first picks randomly an unsatisfied clause and then in a second step, one of the variables with the lowest break count appearing in the selected clause is randomly selected. The break count of a variable is defined as the number of clauses that would be unsatisfied by flipping the chosen variable. If there exists a variable with break count equals to zero, this variable is flipped, otherwise the variable with minimal break count is selected with a certain probability (noise probability).

This is achieved by setting up a binary search tree and proceeding until it either finds a satisfying truth assignment or concludes that no such assignment exists. In each recursive call of the algorithm the propositional formula is simplified by unit propagation. A boolean variable xi is selected according to a predefined rule among the n boolean variables. Next, find all the clauses that include the literal xi and delete it from all these clauses. Let C = {C1,C2, . . ,Ck} be the set of k(<= m) clauses resulting from this process.

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