Related papers: Fully-Dynamic Minimum Spanning Forest with Improve…
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental…
Baswana, Gupta and Sen [FOCS'11] showed that fully dynamic maximal matching can be maintained in general graphs with logarithmic amortized update time. More specifically, starting from an empty graph on $n$ fixed vertices, they devised a…
We consider the problem of maintaining a $(1-\epsilon)$-approximation to the densest subgraph (DSG) in an undirected multigraph as it undergoes edge insertions and deletions (the fully dynamic setting). Sawlani and Wang [SW20] developed a…
Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an…
We give offline algorithms for processing a sequence of $2$ and $3$ edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for $3$-edge and $3$-vertex…
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…
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. We essentially settle the complexity of this…
A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. In this paper we study Minimum Stable Cut, the problem of finding a stable cut of minimum weight. Since this…
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, and it is preferable to perform the computations on a sparse…
We introduce a notion for hierarchical graph clustering which we call the expander hierarchy and show a fully dynamic algorithm for maintaining such a hierarchy on a graph with $n$ vertices undergoing edge insertions and deletions using…
The dynamic trees problem is to maintain a tree under edge updates while supporting queries like connectivity queries or path queries. Despite the first data structure for this fundamental problem -- the link-cut tree -- being invented 40…
It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…
We consider the problem of maintaining an (approximately) minimum vertex cover in an $n$-node graph $G = (V, E)$ that is getting updated dynamically via a sequence of edge insertions/deletions. We show how to maintain a…
In their breakthrough ICALP'15 paper, Bernstein and Stein presented an algorithm for maintaining a $(3/2+\epsilon)$-approximate maximum matching in fully dynamic {\em bipartite} graphs with a {\em worst-case} update time of…
In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal $\min(O(\log n), f)$ approximation factor. (Throughout, $m$, $n$, $f$, and $C$ are parameters denoting the maximum…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
We present new results on a number of fundamental problems about dynamic geometric data structures: 1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or…
Given a simple $n$-vertex, $m$-edge graph $G$ undergoing edge insertions and deletions, we give two new fully dynamic algorithms for exactly maintaining the edge connectivity of $G$ in $\tilde{O}(n)$ worst-case update time and…
We give the first algorithm that maintains an approximate decision tree over an arbitrary sequence of insertions and deletions of labeled examples, with strong guarantees on the worst-case running time per update request. For instance, we…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…