Related papers: Enumerating Minimal Defensive Alliances
Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the…
In the last decade, subgraph detection and enumeration have emerged as a central problem in distributed graph algorithms. This is largely due to the theoretical challenges and practical applications of these problems. In this paper, we…
Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability…
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…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
The problem Defensive $\delta$-Covering, for some covering range $\delta > 0$, is a continuous facility location problem on undirected graphs where all edges have unit length. It is a generalization of Defensive Dominating Set and…
A set $D \subseteq V$ for the graph $G=(V, E)$ is called a dominating set if any vertex $v\in V\setminus D$ has at least one neighbor in $D$. Fomin et al.[9] gave an algorithm for enumerating all minimal dominating sets with $n$ vertices in…
A dominating set $S$ in a graph is a subset of vertices such that every vertex is either in $S$ or adjacent to a vertex in $S$. A minimal dominating set $M$ is a dominating set such that $M-v$ is not a dominating set for all $v \in M$. In…
Despite achieving strong performance in semi-supervised node classification task, graph neural networks (GNNs) are vulnerable to adversarial attacks, similar to other deep learning models. Existing researches focus on developing either…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
A real-world graph has a complex topological structure, which is often formed by the interaction of different latent factors. However, most existing methods lack consideration of the intrinsic differences in relations between nodes caused…
In this paper, we provide a novel enumeration algorithm for the set of all walks of a given length within a directed graph. Our algorithm has worst-case constant delay between outputting succinct representations of such walks, after a…
Distributed gathering algorithms aim to achieve complete visibility graphs via a "never lose a neighbour" policy. We suggest a method to maintain connected graph topologies, while reducing the number of effective edges in the graph to order…
Directly motivated by security-related applications from the Homeland Security Enterprise, we focus on the privacy-preserving analysis of graph data, which provides the crucial capacity to represent rich attributes and relationships. In…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
This work focuses on developing an effective meta-heuristic approach to protect against simultaneous attacks on nodes of a network modeled using a graph. Specifically, we focus on the $k$-strong Roman domination problem, a generalization of…
We consider the following variants of the classical minimum dominating set problem in graphs: locating-dominating set, locating total-dominating set and open locating-dominating set. All these problems are known to be hard for general…
Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…
Adversarial training has gained great popularity as one of the most effective defenses for deep neural network and more generally for gradient-based machine learning models against adversarial perturbations on data points. This paper…
We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that…