A nearly optimal oracle for avoiding failed vertices and edges

  title={A nearly optimal oracle for avoiding failed vertices and edges},
  author={Aaron Bernstein and David R. Karger},
We present an improved oracle for the distance sensitivity problem. The goal is to preprocess a directed graph G = (V,E) with non-negative edge weights to answer queries of the form: what is the length of the shortest path from x to y that does not go through some failed vertex or edge f. The previous best algorithm produces an oracle of size ~O(n2) that has an O(1) query time, and an ~O(n2√m) construction time. It was a randomized Monte Carlo algorithm that worked with high probability. Our… CONTINUE READING
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