We present a new dynamic matching sparsification scheme. From this scheme we derive a
framework for dynamically rounding fractional matchings against adaptive adversaries …

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 …

A maximal independent set (MIS) can be maintained in an evolving m-edge graph by simply
recomputing it from scratch in O (m) time after each update. But can it be maintained in time …

We introduce a new framework for computing approximate maximum weight matchings. Our
primary focus is on the fully dynamic setting, where there is a large gap between the …

We develop the first parallel graph coloring heuristics with strong theoretical guarantees on
work and depth and coloring quality. The key idea is to design a relaxation of the vertex …

A streaming algorithm is considered to be adversarially robust if it provides correct outputs
with high probability even when the stream updates are chosen by an adversary who may …

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 …

Nearly thirty years ago, Bar-Noy, Motwani and Naor [IPL'92] conjectured that an online (1+ o
(1)) Δ-edge-coloring algorithm exists for n-node graphs of maximum degree Δ= ω (log n) …

Graph coloring is a fundamental problem with wide reaching applications in various areas
including ata mining and databases, eg, in parallel query optimization. In recent years, there …