# Properties Of Heuristics

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**Properties of Heuristics Dominance:**

h2 is said to dominate h1 iff h2(n) ≥ h1(n) for any node n.

A* will expand fewer nodes on average using h2 than h1.

**Proof:**

Every node for which f(n) < C* will be expanded. Thus n is expanded whenever

**h(n) < f* - g(n)**

Since h2(n) ≥ h1(n) any node expanded using h2 will be expanded using h1.

**Using multiple heuristics**: Suppose you have identified a number of non-overestimating heuristics for a problem: h1(n), h2(n), … , hk(n)

Then max (h1(n), h2(n), … , hk(n))

is a more powerful non-overestimating heuristic. This follows from the property of dominance