Related papers: Improved Linear-Time Algorithm for Computing the $…
We present the first linear-time algorithm that computes the $4$-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing $4$-edge connectivity. Our results are based on a…
In this work, we present the first linear time deterministic algorithm computing the 4-edge-connected components of an undirected graph. First, we show an algorithm listing all 3-edge-cuts in a given 3-edge-connected graph, and then we use…
We provide a deterministic algorithm for computing the $5$-edge-connected components of an undirected multigraph in linear time. There were probably good indications that this computation can be performed in linear time, but no such…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By…
A graph is componentwise biconnected if every connected component either is an isolated vertex or is biconnected. We present a linear-time algorithm for the problem of adding the smallest number of edges to make a bipartite graph…
We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and…
Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…
We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits. With the same time and using $O(n+m)$ bits, we can compute the…
Given a connected undirected multigraph G (a graph that may contain parallel edges), the algorithm of [19] finds the 3-edge-connected components of $G$ in linear time using an innovative graph contraction technique based on a depth-first…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
Computing edge-connected components in directed and undirected graphs is a fundamental and well-studied problem in graph algorithms. In a very recent breakthrough, Korhonen [STOC 2025] showed that for any fixed $k$, the $k$-edge connected…
Computing the connected components of a graph is a fundamental problem in algorithmic graph theory. A major question in this area is whether we can compute connected components in $o(\log n)$ parallel time. Recent works showed an…
A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of $G$ to a sequence of horizontal…
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We present an efficient…
Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
It is known that the vertex connectivity of a planar graph can be computed in linear time. We extend this result to the class of locally maximal 1-plane graphs: graphs that have an embedding with at most one crossing per edge such that the…
We present a near-linear-time algorithm that, given a bridgeless cubic graph, finds a perfect matching intersecting every 3-edge-cut in exactly one edge. This improves over a cubic algorithm of Boyd et al. for the same problem, and over our…