Path-finding on a grid

Path-finding is an important problem for many applications, including transportation scheduling, robot planning, military simulations, and computer games. Typically, a grid is superimposed over a region, and a graph search is used to find the optimal (minimal cost) path. The most common scenario is to use a grid of tiles and to search using A*. This paper discusses the tradeoffs for different grid representations and grid search algorithms. Grid representations discussed are 4-way tiles, 8-way tiles, and hexes. This paper introduces texes as an efficient representation, of hexes. The search algorithms used are A* and iterative deepening A* (IDA*). Application-dependent properties dictate which grid representation and search algorithm will yield the best results.