Related papers: The Total Acquisition Number of the Randomly Weigh…
Let $G$ be a graph in which each vertex initially has weight 1. In each step, the weight from a vertex $u$ can be moved to a neighbouring vertex $v$, provided that the weight on $v$ is at least as large as the weight on $u$. The total…
Let $G$ be a graph in which each vertex initially has weight 1. In each step, the weight from a vertex $u$ to a neighbouring vertex $v$ can be moved, provided that the weight on $v$ is at least as large as the weight on $u$. The total…
Let $G$ be a graph in which each vertex initially has weight 1. In each step, the unit weight from a vertex $u$ to a neighbouring vertex $v$ can be moved, provided that the weight on $v$ is at least as large as the weight on $u$. The unit…
Let $G$ be a graph with nonnegative integer weights. A {\it unit acquisition move} transfers one unit of weight from a vertex to a neighbor that has at least as much weight. The {\it unit acquisition number} of a graph $G$, denoted…
We study a randomized algorithm for graph domination, by which, according to a uniformly chosen permutation, vertices are revealed and added to the dominating set if not already dominated. We determine the expected size of the dominating…
For an edge-weighted connected undirected graph, the minimum $k$-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into $k$ connected components. The problem is NP-hard when $k$ is part…
We study a random graph $G_n$, which combines aspects of geometric random graphs and preferential attachment. The resulting random graphs have power-law degree sequences with finite mean and possibly infinite variance. In particular, the…
For a finite graph $G=(V,E)$ let $G^*$ be obtained by considering a random perfect matching of $V$ and adding the corresponding edges to $G$ with weight $\varepsilon$, while assigning weight 1 to the original edges of $G$. We consider…
Given an edge-weighted (metric/general) complete graph with $n$ vertices, the maximum weight (metric/general) $k$-cycle/path packing problem is to find a set of $\frac{n}{k}$ vertex-disjoint $k$-cycles/paths such that the total weight is…
A random graph order is a partial order achieved by independently sprinkling relations on a vertex set (each with probability $p$) and adding relations to satisfy the requirement of transitivity. A \textit{post} is an element in a partially…
In the oblivious buy-at-bulk network design problem in a graph, the task is to compute a fixed set of paths for every pair of source-destinations in the graph, such that any set of demands can be routed along these paths. The demands could…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
We study the complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W_n and the number of edges H_n of the minimal weight path between two distinct…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
In recent years, graph neural networks (GNNs) have gained increasing popularity and have shown very promising results for data that are represented by graphs. The majority of GNN architectures are designed based on developing new…