ERA*: Enhanced Relaxed A* algorithm for Solving the Shortest Path Problem in Regular Grid Maps

TL;DR

This paper presents ERA*, an efficient algorithm for shortest path problems in regular grid maps, offering significant improvements in speed and memory usage over existing algorithms like RA* and A* through a novel lookup matrix approach.

Contribution

ERA* generalizes Hadlock's algorithm to G8 grids, achieving faster computation and reduced memory requirements while maintaining solution optimality compared to RA*.

Findings

ERA* is 2.25 times faster than RA* on average.

ERA* is 17 times faster than A* on average.

ERA* requires less memory by not storing G score matrices.

Abstract

This paper introduces a novel algorithm for solving the point-to-point shortest path problem in a static regular 8-neighbor connectivity (G8) grid. This algorithm can be seen as a generalization of Hadlock algorithm to G8 grids, and is shown to be theoretically equivalent to the relaxed $A^*$ ($RA^*$) algorithm in terms of the provided solution's path length, but with substantial time and memory savings, due to a completely different computation strategy, based on defining a set of lookup matrices. Through an experimental study on grid maps of various types and sizes (1290 runs on 43 maps), it is proven to be 2.25 times faster than $RA^*$ and 17 times faster than the original $A^*$, in average. Moreover, it is more memory-efficient, since it does not need to store a G score matrix.