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By Witold Bednorz

ISBN-10: 9537619273

ISBN-13: 9789537619275

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23] G. R. Cantieni, G. Iannaccone, C. Barakat, C. Diot and P. Thiran, “Reformulating the monitor placement problem: optimal network-wide sampling, In Proceedings of CoNEXT06, Lisboa, Portugal, December, 2006. [24] M. R. Garey and D. S. Johnson. “Computers and Intractability: A Guide to the Theory of NP-Completeness”. H. Freeman Publishing Company, 1979. 38 Advances in Greedy Algorithms [25] Y. Bejerano abd R. Rastogi, “Robust monitoring of link delays and faults in IP networks”. IEEE/ACM Trans.

All clauses are satisfied, the algorithm returns a satisfying assignment. If neither of these two situations occur, an unassigned variable is chosen and the algorithm is called recursively after adding a unit clause containing this variable and its negation. If all branches are explored and no satisfying assignment has been reached, the formula is found to be unsatisfiable. For efficiency reasons, the search tree is explored in depth-first search manner. Since we are only interested in whether the SAT problem is satisfiable or not, we stop as soon as the first solution is found.

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.

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Advances in Greedy Algorithms by Witold Bednorz

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