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 uninformed 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. 0 1992 John Wiley & Sons, Inc.
Various reports of brain wave synchrony during Transcendental Meditation have appeared in the literature and have been interpreted as indicating a heightened state of integration of brain function. We suggest that this observed synchrony rather than indicating a greater integration of brain function might be an artifact of parts of the brain acting like a finite state machine. The finite state model is developed, its properties derived and a test for the hypothesis is presented.
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