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The number of children of a node in a search tree, or an upper bound on that number over the tree. With branching factor at most $b$ and depth at most $d$, a complete traversal visits at most $1+b+\cdots +b^d$ nodes.

Choose an unassigned variable with the fewest currently legal values. No legal values detects failure immediately; exactly one legal value forces a choice. This ordering can reduce the search tree without changing the set of solutions.

Discarding a branch of a search tree after proving that no completion can satisfy the constraints or improve the current best solution. For minimization, a lower bound on every completion justifies pruning when it is at least the best value already found; this is the principle behind branch and bound.