Three path-planning algorithms for single-pair path computation are evaluated. These algorithms are the iterative breath-first search, Dijkstra's single-source path-planning algorithm, and the A* single-path planning algorithm. The performance of the algorithms is evaluated on graphs representing the roadmap of Minneapolis. In order to get an insight into their relative performance, synthetic grid maps are used as a benchmark computation. The effects of two parameters, namely path length and edge-cost-distribution, on the performance of the algorithms are examined. The effects of implementation decisions on the performance of the A* algorithm are discussed. The main hypothesis is that estimator functions can improve the average-case performance of single-pair path computation when the length of the path is small compared to the diameter of the graph. This hypothesis is examined using experimental studies and analytical cost modeling. >