By Witold Bednorz
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These include techniques such as Simulated Annealing , Evolutionary Algorithms , and Greedy Randomized Adaptive Search Procedures . 3. The GSAT greedy algorithm This section is devoted to explaining the GSAT greedy algorithm and one of its variants before embedding it into the multilevel paradigm. Basically, the GSAT algorithm begins with a randomly generated assignment of the variables, and then uses the steepest descent 42 Advances in Greedy Algorithms heuristic to find the new truth value assignment which best decreases the number of unsatisfied clauses.
The graph G (I)(V,E) for the given instance of the SC problem. 1 Hardness of the LM and WLM problems Theorem 1 The LM and WLM problems are NP-hard, even when the routing tree (RT) of each node is restricted to be its shortest path tree (SPT). 23 A Greedy Scheme for Designing Delay Monitoring Systems of IP Networks Fig. 2. The RTs of nodes r(2), and s1. Proof: We show that the LM problem is NP-hard by presenting a polynomial reduction from the set cover problem to the LM problem. From this follows that also the WLM problem is NP-hard.
I). 24 Advances in Greedy Algorithms Next, we show that if there is a set of at most k+m+1 stations that covers all the graph edges then there is a solution for the SC problem of size at most k. g that the selected stations are r(2) and for each element zi. None of these m + 1 stations covers edges (ui,wi) for elements zi ∈ Z. 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.
Advances in Greedy Algorithms by Witold Bednorz