Improved distance sensitivity oracles with subcubic preprocessing time

We consider the problem of building distance sensitivity oracles (DSOs). Given a directed graph G = ( V , E ) with edge weights in { 1 2 … M } we need to preprocess it into data structure, and answer following queries: given vertices u v ∈ failed vertex or f ∪ output length shortest path from that does not go through . Our main result is simple DSO O ˜ n 2.7233 preprocessing time query time. Moreover, if input undirected, can be improved 2.6865 The algorithm randomized correct probability ≥ − / C for constant made arbitrarily large. This improves previous best 2.8729 polylog [STOC'20].