Heuristic dominance

A heuristic function $h_2$ dominates $h_1$ if $h_2(s)\ge h_1(s)$ everywhere. When both are admissible heuristics, the larger estimate is at least as informative for A-star search: for a fixed accumulated path cost $g$ and optimal solution cost $C^{\ast }$, $g+h_2<C^{\ast }$ implies $g+h_1<C^{\ast }$. This compares the compulsory search region, not arbitrary tie handling at $C^{\ast }$, evaluation overhead or wall-clock time.