Related papers: Engineering Fully Dynamic Exact $\Delta$-Orientati…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions. While there has been theoretical work on this problem, our algorithm is the first…
In edge orientations, the goal is usually to orient (direct) the edges of an undirected $n$-vertex graph $G$ such that all out-degrees are bounded. When the graph $G$ is fully dynamic, i.e., admits edge insertions and deletions, we wish to…
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…
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…
We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations…
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…
There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for…
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…
Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and insertions. It is one of the most…
We study the fully dynamic maximum matching problem. In this problem, the goal is to efficiently maintain an approximate maximum matching of a graph that is subject to edge insertions and deletions. Our focus is on algorithms that maintain…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
In the fully dynamic edge connectivity problem, the input is a simple graph $G$ undergoing edge insertions and deletions, and the goal is to maintain its edge connectivity, denoted $\lambda_G$. We present two simple randomized algorithms…
A low out-degree orientation directs each edge of an undirected graph with the goal of minimizing the maximum out-degree of a vertex. In the parallel batch-dynamic setting, one can insert or delete batches of edges, and the goal is to…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\"ive solution is to iteratively find the densest subgraph and remove it in…
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions…
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 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…