Abstract:A graph algorithm is truly subquadratic if it runs in O(m b ) time on connected m-edge graphs, for some positive b < 2. Roditty and Vassilevska Williams (STOC'13) proved that under plausible complexity assumptions, there is no truly subquadratic algorithm for computing the diameter of general graphs. In this work, we present positive and negative results on the existence of such algorithms for computing the diameter on some special graph classes. Specifically, three vertices in a graph form an asteroidal tripl… Show more
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