In recent years, a new “fine-grained” theory of computational hardness has been developed,
based on “fine-grained reductions” that focus on exact running times for problems …

All-Pairs Shortest Paths (APSP) is one of the most basic problems in graph algorithms.
Given an n-node directed or undirected graph with integer weights in {-nc,..., nc} and no …

Abstract The Orthogonal Vectors problem (OV) asks: given n vectors in {0, 1} O (log n), are
two of them orthogonal? OV is easily solved in O (n 2 log n) time, and it is a central problem …

In this paper, we design efficient algorithms to approximately count the number of edges of a
given k-hypergraph, and to sample an approximately uniform random edge. The hypergraph …

A line of work has shown how nontrivial uniform algorithms for analyzing circuits can be
used to derive non-uniform circuit lower bounds. We show how the non-existence of …

The goal of the paper is to give fine-grained hardness results for the Subgraph Isomorphism
(SI) problem for fixed size induced patterns H, based on the k-Clique hypothesis that the …

We study finding and listing $ k $-cliques in a graph, for constant $ k\geq 3$, a fundamental
problem of both theoretical and practical importance. Our main contribution is a new output …

The All-Pairs Shortest Paths (APSP) problem is one of the most basic problems in computer
science. The fastest known algorithms for APSP in n-node graphs run in n 3− o (1) time, and …

This study examines the time complexities of the unbalanced optimal transport problems
from an algorithmic perspective for the first time. We reveal which problems in unbalanced …

We show by reduction from the Orthogonal Vectors problem that algorithms with strongly
subquadratic running time cannot approximate the Fréchet distance between curves better …