We present a new technique for efficiently removing almost all short cycles in a graph
without unintentionally removing its triangles. Consequently, triangle finding problems do …

Roundtrip spanners are the analog of spanners in directed graphs, where the roundtrip
metric is used as a notion of distance. Recent works have shown existential results of …

We present several new efficient algorithms for approximating the girth, g, of weighted and
unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially …

In this paper we provide a Õ (n 2) time algorithm that computes a 2-multiplicative
approximation of the girth of an n-node m-edge directed graph with non-negative edge …

It is known that a better than $2 $-approximation algorithm for the girth in dense directed
unweighted graphs needs $ n^{3-o (1)} $ time unless one uses fast matrix multiplication …

We consider the directed minimum weight cycle problem in the fully dynamic setting. To the
best of our knowledge, so far no fully dynamic algorithms have been designed specifically …

Computing the diameter of a graph, ie the largest distance, is a fundamental problem that is
central in fine-grained complexity. In undirected graphs, the Strong Exponential Time …

Processing a reachability query in large-scale networks using existing methods remains one
of the most challenging problems in graph mining. In this paper, we propose a novel …

Given an n-vertex m-edge graph G with nonnegative edge-weights, a shortest cycle is one
minimizing the sum of the weights on its edges. The girth of G is the weight of a shortest …

Graph spanners are a sparse subgraph of a graph such that shortest-path distances for all
pairs of vertices are approximately preserved with a factor called stretch, and roundtrip …