Heuristic paper “A Formal Basis for the Heuristic Determination of Minimum Cost Paths”, Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. Definitions For any subgraph \(G_s\) and any goal set \(T\) and starting state \(s\): Let \(f^*(n)\) be the actual cost of an optimal path constrained through \(n\), from \(s\) to \(n\) to a preferred goal node \(n\). From this definition, the (‘unconstrained’) optimal path can be written as \(f^*(s) = h^*(s)\), where \(h^*(n)\) is the optimal path from node \(n\) to the preferred goal node of \(s\).