As many readers may know, graph theory is a fundamental branch of mathematics that
explores networks made up of nodes and edges, focusing on their paths, structures, and …

We give algorithms for finding the k shortest paths (not required to be simple) connecting a
pair of vertices in a digraph. Our algorithms output an implicit representation of these paths …

In 1900, less than 20 percent of the world population lived in cities, in 2007, just more than
50 percent of the world population lived in cities. In 2050, it has been predicted that more …

We propose fully dynamic algorithms for maintaining the distances and the shortest paths
from a single source in either a directed or an undirected graph with positive real edge …

An information retrieval (IR) engine can rank documents based on textual proximity of
keywords within each document. In this paper we apply this notion to search across an …

In this work we revisit the fundamental Single-Source Shortest Paths (SSSP) problem with
possibly negative edge weights. A recent breakthrough result by Bernstein, Nanongkai and …

Computing optimal routes in road networks is one of the showpieces of realworld
applications of algorithmics. In principle, we could use Dijkstra's algorithm—the …

The shortest path problem is one of the most classical algorithm issues in graph theory,
aiming to find the shortest path between the two nodes in a network. It is widely used to …

We consider the problem of finding an obstacle-avoiding path between two points s and t in
the plane, amidst a set of disjoint polygonal obstacles with a total of n vertices. The length of …

Let G=(V, E, w) be a simple digraph, in which all edge weights are nonnegative real
numbers. Let G^ ′ be obtained from G by an application of a set of edge weight updates to …