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Weighted A*
Weighted A* (WA*) trades optimality for speed by inflating the heuristic with a weightw ≥ 1, producing paths that are at most w-times the optimal cost while dramatically reducing the nodes expanded.
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The key idea
Standard A* uses f(n) = g(n) + h(n). Weighted A* instead evaluates f(n) = g(n) + w·h(n). When w = 1 you get classic A*; as w grows the search becomes more greedy, expanding fewer nodes at the cost of solution quality.
The bounded sub-optimality guarantee is the property that makes WA* useful in practice: you can choose exactly how much quality you are willing to sacrifice and get a hard upper bound in return.