Preprint claims faster algorithms for 3SUM and all-pairs shortest paths

An arXiv preprint claims the first polynomial improvements over textbook algorithms for 3SUM, which searches for three numbers summing to zero, and all-pairs shortest paths, which finds routes between every pair of graph vertices. The authors give deterministic running times of O(n^1.9992) for 3SUM on polynomial-size integers and O(n^2.9995) for directed graphs with polynomially bounded integer weights. They say the results refute the corresponding computational hypotheses. The method computes selected entries of thin matrix products by modifying a rectangular matrix multiplication algorithm. The results establish theoretical running-time improvements under the stated input restrictions.