We consider the point-to-point (approximate) shortest-path query problem, which is the
following generalization of the classical single-source (SSSP) and all-pairs shortest-path …

A comprehensive update of the leading algorithms text, with new material on matchings in
bipartite graphs, online algorithms, machine learning, and other topics. Some books on …

Let G=(V, E) be an undirected weighted graph with| V|= n and| E|= m. Let k≥ 1 be an
integer. We show that G=(V, E) can be preprocessed in O (kmn 1/k) expected time …

We present a new randomized method for computing the min-plus product (aka, tropical
product) of two n× n matrices, yielding a faster algorithm for solving the all-pairs shortest …

Before there were computers, there were algorithms. But now that there are computers, there
are even more algorithms, and algorithms lie at the heart of computing. This book provides a …

We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for
weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first …

We say an algorithm on n× n matrices with entries in [-M, M](or n-node graphs with edge
weights from [-M, M]) is truly subcubic if it runs in O (n 3-δ-poly (log M)) time for some δ> 0 …

We present a fast algorithm for the subset convolution problem: given functions f and g
defined on the lattice of subsets of an n-element set n, compute their subset convolution f* g …

Let A and B two n× n matrices over a ring R (eg, the reals or the integers) each containing at
most m nonzero elements. We present a new algorithm that multiplies A and B using O (m …

In the first part of the paper, we reexamine the all-pairsshortest paths (APSP) problem and
present a newalgorithm with running time approaching O (n3/log2n), which improves all …