By Bednorz W.
Bednorz W. Advances in grasping algorithms (In-Teh, 2008)(ISBN 9537619273)(596s)_CsAl_
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The other k monitoring stations are placed in the nodes ui,wi and sj. In order to cover edge (ui,wi), there needs to have a station at one of the nodes ui, wi or sj for some set Qj containing element zi. Also, observe that the RTs of ui and wi cover only edge (ui,wi) for element zi and no other element edges. Similarly, the RT of sj covers only edges (ui,wi) for elements zi contained in set Qj . Let S be a collection of sets defined as follows. For every monitoring station at any node sj add the set Qj ∈ Q to S, and for every monitoring station at any node ui or wi we add to S an arbitrary set Qj ∈ Q such that zi ∈ Qj .
In our model, we assume that packets are forwarded using standard IP forwarding, that is, each node relies exclusively on the destination address in the packet to determine the next hop. Thus, for every node x ∈ Ps,t, Px,t is included in Ps,t. In addition, we also assume that Ps,t is the routing path in the opposite direction from node t to node s. This, in turn, implies that for every node x ∈ Ps,t, Ps,x is a prefix of Ps,t. As a consequence, it follows that for every node s ∈ V , the subgraph obtained by merging all the paths Ps,t, for every t ∈ V , must have a tree topology.
1 Systematic search algorithms The most popular and efficient systematic search algorithms for SAT are based on the DavisPutnam (DP)  procedure which enumerates all possible variable assignments. 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.