This survey provides a guiding reference to researchers seeking an overview of the large
body of literature about graph spanners. It surveys the current literature covering various …

We present a Las Vegas algorithm for dynamically maintaining a minimum spanning forest
of an nnode graph undergoing edge insertions and deletions. Our algorithm guarantees an …

Designing dynamic graph algorithms against an adaptive adversary is a major goal in the
field of dynamic graph algorithms. While a few such algorithms are known for spanning …

Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-
case guarantee. But amortized data structures are not suitable for real-time systems, where …

We develop a framework for graph sparsification and sketching, based on a new tool, short
cycle decomposition, which is a decomposition of an unweighted graph into an edge-disjoint …

Consider the following distance query for an n-node graph G undergoing edge insertions
and deletions: given two sets of nodes I and J, return the distances between every pair of …

Maintaining and updating shortest paths information in a graph is a fundamental problem
with many applications. As computations on dense graphs can be prohibitively expensive …

This article studies the fundamental problem of graph coloring in fully dynamic graphs. Since
the problem of computing an optimal coloring, or even approximating it to within n1-ε for any …

We (nearly) settle the time complexity for computing vertex fault-tolerant (VFT) spanners with
optimal sparsity (up to polylogarithmic factors). VFT spanners are sparse subgraphs that …

Submodular maximization under matroid and cardinality constraints are classical problems
with a wide range of applications in machine learning, auction theory, and combinatorial …