Combinatoric Explosion

Suppose that each node of a search tree has b descendants; this is sometimes called the average branching factor.[Real search trees often have different numbers of descendants from different nodes.] Then the number of nodes at the bottom of a tree d plies deep is bd. This number grows exponentially with depth and can quickly become very large as the search becomes deeper; this rapid growth is called the combinatoric explosion problem.

The maximum depth, i.e. maximum number of steps between any two states, is called the diameter of the problem space.

In chess, there may be 30 possible moves from each state. A chess tree 10 plies deep would require searching 3010 or nearly 1015 nodes. On a computer that could examine one node in a microsecond, it would take over 18 years of computer time to examine this tree.

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