Contents • • • • • • • • • • • • • Summary [ ] The algorithm stores intervals for nodes of the as opposed to single point-valued estimates. Then, leaf nodes of the tree can be searched until one of the top level nodes has an interval which is clearly 'best.' Details [ ] Interval evaluations rather than estimates [ ] Leaf nodes of a B*-tree are given evaluations that are intervals rather than single numbers. The interval is supposed to contain the true value of that node. If all intervals attached to leaf nodes satisfy this property, then B* will identify an optimal path to the goal state. Backup process [ ] To back up the intervals within the tree, a parent's upper bound is set to the maximum of the upper bounds of the children. A parent's lower bound is set to the maximum of the lower bound of the children. Travian Server Script Download Files.

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Note that different children might supply these bounds. Termination of search [ ] B* systematically expands nodes in order to create 'separation,' which occurs when the lower bound of a direct child of the root is at least as large as the upper bound of any other direct child of the root. A tree that creates separation at the root contains a proof that the best child is at least as good as any other child. In practice, complex searches might not terminate within practical resource limits. So the algorithm is normally augmented with artificial termination criteria such as time or memory limits.

When an artificial limit is hit, then you must make a heuristic judgment about which move to select. Normally, the tree would supply you with extensive evidence, like the intervals of root nodes. Expansion [ ] B* is a best-first process, which means that the whole tree is kept in memory, and repeatedly descended to find a leaf to expand. This section describes how to choose the node to expand.

At the root of the tree, the algorithm applies one of two strategies, called prove-best and disprove-rest. In the prove-best strategy, the algorithm selects the node associated with the highest upper bound.

The hope is that expanding that node will raise its lower bound higher than any other node's upper bound. The disprove-rest strategy selects the child of the root that has the second-highest upper bound. The hope is that by expanding that node you might be able to reduce the upper bound to less than the lower bound of the best child. Strategy selection [ ] Note that applying the disprove-rest strategy is pointless until the lower bound of the child node that has the highest upper bound is the highest among all lower bounds. The original algorithm description did not give any further guidance on which strategy to select. There are several reasonable alternatives, such as expanding the choice that has the smaller tree.

Strategy selection at non-root nodes [ ] Once a child of the root has been selected (using prove-best or disprove-best) then the algorithm descends to a leaf node by repeatedly selecting the child that has the highest upper bound. When a leaf node is reached, the algorithm generates all successor nodes and assigns intervals to them using the evaluation function. Then the intervals of all nodes have to be backed up using the backup operation. When transpositions are possible, then the back-up operation might need to alter the values of nodes that did not lie on the selection path.