The A* Algorithm is a variation on the Lee Algorithm that reduces execution time during the expansion phase by biasing the search in the direction of the target. Unlike the Lee Algorithm, which uses the distance from the source as its cost function, Hadlock’s algorithm uses a value known as a cost
f = g + h
where g is the distance of a labeled grid from the source (i.e., the cost used in the Lee algorithm), and h is an estimate of the cost from the labeled gridpoint to the target (i.e., the Manhattan distance from the gridpoint to the target). Thus nodes that are closer to the target have lower costs than nodes that are further from the target. Since the expansion algorithm selects nodes with the lowest cost for expansion, this biases the search in the direction of the target. When an obstacle is reached, a detour is necessary and nodes labeled with higher values are expanded. The backtrace phase operates identically to the Lee Algorithm.
Because it still does exhaustive search as a fallback, the A* algorithm still guarantees that a minimum-cost connection will be found if it exists.
References
F. Rubin, “The Lee path connection algorithm”, IEEE Transactions on Computers, Vol. C-23, 1974, pp 907 – 914.
Wikipedia, “A* search algorithm“, February 2007.