Related papers: Dynamic Maintenance of Low-Stretch Probabilistic T…
We give a Las Vegas data structure which maintains a minimum spanning forest in an n-vertex edge-weighted dynamic graph undergoing updates consisting of any mixture of edge insertions and deletions. Each update is supported in O(n^{1/2 -…
Probabilistic metric embedding into trees is a powerful technique for designing online algorithms. The standard approach is to embed the entire underlying metric into a tree metric and then solve the problem on the latter. The overhead in…
We give the first non-trivial decremental dynamic embedding of a weighted, undirected graph $G$ into $\ell_p$ space. Given a weighted graph $G$ undergoing a sequence of edge weight increases, the goal of this problem is to maintain a…
Metric embeddings into structured spaces, particularly hierarchically well-separated trees (HSTs), are a fundamental tool in the design of online algorithms. In the classical online embedding setting, points arrive sequentially and must be…
We develop a new algorithmic framework for designing approximation algorithms for cut-based optimization problems on capacitated undirected graphs that undergo edge insertions and deletions. Specifically, our framework dynamically maintains…
This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a graph which strongly preserves distances in the graph is a…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
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…
We present a new distance oracle in the fully dynamic setting: given a weighted undirected graph $G=(V,E)$ with $n$ vertices undergoing both edge insertions and deletions, and an arbitrary parameter $\epsilon$ where $\epsilon\in[1/\log^{c}…
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…
The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore…
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…
We develop the first fully dynamic algorithm that maintains a decision tree over an arbitrary sequence of insertions and deletions of labeled examples. Given $\epsilon > 0$ our algorithm guarantees that, at every point in time, every node…
The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…
In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…
We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs. For instance, it is known how to maintain a 1/2-approximate matching in $\log^{O(1)} n$…
Algebraic data structures are the main subroutine for maintaining distances in fully dynamic graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot maintain the shortest paths, especially against adaptive…
We give improved algorithms for maintaining edge-orientations of a fully-dynamic graph, such that the out-degree of each vertex is bounded. On one hand, we show how to orient the edges such that the out-degree of each vertex is proportional…
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the…
This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the…