We consider the classical Minimum Balanced Cut problem: given a graph G, compute a
partition of its vertices into two subsets of roughly equal volume, while minimizing the …

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 …

Refactorings are behavior-preserving program transformations that automate design
evolution in object-oriented applications. Three kinds of design evolution are: schema …

We present two algorithms for dynamically maintaining a spanning forest of a graph
undergoing edge insertions and deletions. Our algorithms guarantee worst-case update …

We give a Las Vegas data structure which maintains a minimum spanning forest in an n-
vertex edge-weighted undirected dynamic graph undergoing updates consisting of any …

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 initiate the study of matroid problems in a new oracle model called dynamic oracle. Our
algorithms in this model lead to new bounds for some classic problems, and a “unified” …

Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms.
We present a randomized Las Vegas dynamic connectivity data structure with 𝑂 (log 𝑛 (log …

Popular fine-grained hypotheses have been successful in proving conditional lower bounds
for many dynamic problems. Two of the most widely applicable hypotheses in this context …

We revisit the vertex-failure connectivity oracle problem. This is one of the most basic graph
data structure problems under vertex updates, yet its complexity is still not well-understood …