Related papers: A New Dynamic Algorithm for Densest Subhypergraphs
We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…
Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…
Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$, the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that has the maximum weighted coverage by \emph{sampling only a few hyperedges} in…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
We present a simple randomized algorithm that can efficiently maintain a $(\Delta+1)$ coloring as the graph undergoes edge insertion and deletion updates, where $\Delta$ denotes an upper bound on the maximum degree. A key advantage is the…
We study the dynamic connectivity problem for massive, dense graphs. Our goal is to build a system for dense graphs that simultaneously answers connectivity queries quickly, maintains a fast update throughput, and a uses a small amount of…
Single Source Shortest Paths ($\textrm{SSSP}$) is among the most well-studied problems in computer science. In the incremental (resp. decremental) setting, the goal is to maintain distances from a fixed source in a graph undergoing edge…
We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three…
The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex…
The problem of finding the degeneracy of a graph is a subproblem of the k-core decomposition problem. In this paper, we present a (1 + epsilon)-approximate solution to the degeneracy problem which runs in O(n log n) time, sublinear in the…
We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous…
A well-known problem in data science and machine learning is {\em linear regression}, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression require at least a linear…
Finding dense subnetworks, with density based on edges or more complex structures, such as subgraphs or $k$-cliques, is a fundamental algorithmic problem with many applications. While the problem has been studied extensively in static…
In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart…
We study maximum matchings in fully dynamic graphs, which are graphs that undergo both edge insertions and deletions. Our focus is on algorithms that estimate the size of maximum matching after each update while spending a small time. An…
We consider dynamic algorithms for maintaining Single-Source Reachability (SSR) and approximate Single-Source Shortest Paths (SSSP) on $n$-node $m$-edge directed graphs under edge deletions (decremental algorithms). The previous fastest…
We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for $(\Delta+1)$- vertex coloring and…
{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…
Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…
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…