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Heuristic sampling on backtrack trees
Current methods for solving many combinatorial problems rely on exhaustively searching the set of all possibilities. Unfortunately, this brute-force approach may be completely impractical if the search space is large. Therefore, knowing the cost of the search program before actually running it can be very useful in practical situations. In addressing the feasibility issue, Knuth (1975) has introduced a method for estimating properties of the backtrack tree by exploring randomly selected paths. In all the experiments conducted, he was able to estimate the size (number of nodes) of the search trees with reasonable accuracy, thereby determining the feasibility of the corresponding backtrack programs. Heuristic sampling is essentially a generalization of Knuth's algorithm. We generalize the simple method by exploiting possible structures among the subtrees through the use of domain-specific knowledge. It turns out that with the aid of simple heuristics, this general method can produce significantly more accurate estimates than the previous method. In fact, this generalized procedure can also be used simultaneously to approximate the original optimization problem, thus making it doubly useful.
- "Current methods for solving many combinatorial problems rely on exhaustively searching the set of all possibilities. Unfortunately, this brute-force approach may be completely impractical if the search space is large. Therefore, knowing the cost of the search program before actually running it can be very useful in practical situations. In addressing the feasibility issue, Knuth (1975) has introduced a method for estimating properties of the backtrack tree by exploring randomly selected paths. In all the experiments conducted, he was able to estimate the size (number of nodes) of the search trees with reasonable accuracy, thereby determining the feasibility of the corresponding backtrack programs. Heuristic sampling is essentially a generalization of Knuth's algorithm. We generalize the simple method by exploiting possible structures among the subtrees through the use of domain-specific knowledge. It turns out that with the aid of simple heuristics, this general method can produce significantly more accurate estimates than the previous method. In fact, this generalized procedure can also be used simultaneously to approximate the original optimization problem, thus making it doubly useful."@en
- "Heuristic sampling on backtrack trees"@en
- "Heuristic sampling on backtrack trees"