Related papers: Incremental Maintenance of Maximal Cliques in a Dy…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of $n$ nodes is vertex-partitioned among $k$ players that…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
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…
Building on existing algorithms and results, we offer new insights and algorithms for various problems related to detecting maximal and maximum bicliques. Most of these results focus on graphs with small maximum degree, providing improved…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In…
A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…
We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…
In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
We analyze the problem of identifying large cliques in graphs that are affected by adversarial uncertainty. More specifically, we consider a new formulation, namely the adversarial maximum clique problem, which extends the classical…
In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…
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…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.
We propose a fully dynamic algorithm for maintaining reachability information in directed graphs. The proposed deterministic dynamic algorithm has an update time of $O((ins*n^{2}) + (del * (m+n*log(n))))$ where $m$ is the current number of…
Finding the shortest path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has been successfully attempted on this problem, most of which is limited to static graphs.…
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…