Level graphs and approximate shortest path algorithms

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Abstract
Shortest path algorithms for graphs have been widely studied and are of great practical utility. For the case of a general graph, Dijkstra's algorithm is known to be optimal. However, in many practical instances, there is a “level” structure which may be imposed on the underlying graph. Utilizing these levels, this paper demonstrates that the time complexity of shortest path generation may be greatly reduced.A new graph structure, the level graph, together with a simple uniformed heuristic, LGS, for searching that structure is introduced, which allows for rapid generation of approximate shortest paths. LGS is studied both analytically and via simulation. It is shown that the length of the path produced by LGS converges rapidly to that of the actual shortest path as the distance between the points increases.