By Witold Bednorz
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Thiran, “Active Measurement for Multiple Link Failures Diagnosis in IP Networks, In Proceedings of PAM’04, Antibes, France, 2004.  K. Suh, Y. Guo, J. F. Kurose, D. F. Towsley, Locating network monitors: Complexity, heuristics, and coverage, In Proceedings of Infocom’05, Miami, FL, USA, March, 2004.  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.
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. The size of the search tree depends on the branching rule adopted (how to select the branch variable) thereby affecting the overall efficiency of DP. This has led to the development of various improved DP variants which differ in the schemes employed to maximize the efficiency of unit propagation in their branching rules.
Since we have two choices for each boolean variable, and taken over n variables, the size of the search space S is |S| = 2n. The chapter is organized as follows. In Section 2 we review various algorithms for SAT problems. Section 3 explains the basic greedy GSAT algorithm. In Section 4, the multilevel paradigm is described. Section 5 presents the multilevel greedy algorithm. In Section 6, we look at the results from testing the new approach on a test suit of problem instances. Finally in Section 7 we give a summary of the work.