This literary review examines pathfinding on regular grid maps. Regular grid maps are common in many applications of pathfinding, such as robotics and video games, and they pose a challenging problem to traditional solutions such as the A* algorithm, slowing down its execution. For this reason there are many algorithms optimized for grid maps to yield better performance than A*.

In this paper we first go over the relevant basics of pathfinding --- Dijkstra's algorithm and its extension, A* --- by examining their pseudocode representations and running time properties. We then introduce three algorithms optimized for pathfinding on grid maps: Hierarchical Path-Finding A*, Rectangular Symmetry Reduction and Jump Point Search. We describe the operation of these algorithms and compare their performance to A* and other algorithms.

We conclude that out of the presented algorithms, Jump Point Search appears to be the best choice considering its performance and other properties. It performs an order of magnitude faster than the A* algorithm used as the baseline, it is faster or at least as fast as the other examined algorithms, and it has no appreciable downsides. We also suggest two possible directions for further research.