By Witold Bednorz

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40 Advances in Greedy Algorithms 2. Methods for SAT The SAT problem has been extensively studied due to its simplicity and applicability. The simplicity of the problem coupled with its intractability makes it an ideal platform for exploring new algorithmic techniques. This has led to the development of many algorithms for solving SAT problems which usually fall into two main categories: systematic algorithms and local search algorithms. Systematic search algorithms are guaranteed to return a solution to a SAT problem if at least one exists or prove it insoluble otherwise.

V = V {r1, r2, r3, r4, r5} and the edges E = E {(v, r1)│v ∈ V} {(r1, r2), (r1, r3), (r1, r4), (r1, r5), (r2, r3), (r4, r5)}. The weight of every edge e ∈ E is 3 and the weight of any edge e ∉ E is 2. In the following R = {r1, r2, r3, r4, r5}. An example of such graph is given in Figure 8. Now we will show that the given VC instance, graph G(V,E), has a solution, S of size k if and only if the PM instance, graph G ( V , E ) has a solution, S of size k + 2. In this proof we assume without lose of generality that the routing tree (RT) of every node is its shortest path tree (SPT).

A drawback of this approach is that the accuracy of a path delay estimation decreases as the number of links that compose the path increases. A better estimate can be achieved by partitioning each path into a few contiguous segments. Each segment is then required to be in the RT of a single monitoring station, which estimates its delay by sending two probe messages to the segment's end-points. Of course, the best estimate of delay is obtained when every path consists of a single segment. 1 cannot guarantee an upper bound on the number of segments in a path.

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