Which of the following best describes the node that a Greedy Best-First Search…

Greedy Best-First Search (GBFS) is an informed search strategy that evaluates every frontier node using the evaluation function f(n) = h(n), where h(n) is a heuristic estimate of the remaining cost from node n to the goal. At each step it expands whichever frontier node currently has the smallest h(n) value, never considering depth, path length so far, or actual distance travelled — only the heuristic estimate attached to each candidate node.

For instance, if the frontier holds node P with h(P) = 6 and node Q with h(Q) = 3, GBFS expands Q next purely because 3 is smaller than 6, regardless of how deep P or Q sit in the search tree and regardless of whether Q is truly nearer the goal, since h(n) is only an estimate and a poorly designed heuristic can mislead it. Matching this operational rule to the options given, the exact criterion GBFS uses to pick the next node for expansion is minimum heuristic cost.

Comparing each option against this rule:

• Shallowest is the expansion rule used by Breadth-First Search, which processes nodes level by level with a FIFO queue and never consults any heuristic.

• Deepest is the expansion rule used by Depth-First Search, which follows one branch as far as possible using a stack (LIFO), again without any heuristic.

• The one close to the goal node restates the everyday intuition behind the heuristic, but actual distance to the goal cannot be measured mid-search — only the heuristic's estimate can be, so this phrasing is too imprecise to be the operational rule.

• Minimum heuristic cost is the precise rule: the node with the least h(n) is the one expanded, matching the definition of Greedy Best-First Search exactly.