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It has been shown that there exists a transition in the average-case complexity of tree search problems, from exponential to polynomial in the search depth. We develop a new method, called -transformation, which makes use of this complexity transition, to find a suboptimal solution. With a random tree model, we show that, as the tree depth approaches infinity, the expected number of nodes expanded...
The traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems. Branch-and-bound (BnB) is the best method for finding an optimal solution of the TSP. Previous research has shown that there exists a transition in the average computational complexity of BnB on random trees. We show experimentally that when the intercity distances of the asymmetric TSP are drawn...
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