Related papers: A practical algorithm for 3-admissibility
Consider an undirected graph $G = (VG, EG)$ and a set of six \emph{terminals} $T = \set{s_1, s_2, s_3, t_1, t_2, t_3} \subseteq VG$. The goal is to find a collection $\calP$ of three edge-disjoint paths $P_1$, $P_2$, and $P_3$, where $P_i$…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
In real-world scenarios, although data entities may possess inherent relationships, the specific graph illustrating their connections might not be directly accessible. Latent graph inference addresses this issue by enabling Graph Neural…
A well known theorem in graph theory states that every graph $G$ on $n$ vertices and minimum degree at least $d$ contains a path of length at least $d$, and if $G$ is connected and $n\ge 2d+1$ then $G$ contains a path of length at least…
Network inference is the process of deciding what is the true unknown graph underlying a set of interactions between nodes. There is a vast literature on the subject, but most known methods have an important drawback: the inferred graph is…
As a result of the interaction of rapid development and competition in information technologies, the reliability of a network and how solid it remains is important. It is called the hat vulnerability of the network to measure the endurance…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
The reliability of a network is an important parameter to consider when building a network. Different characteristics of the network can become unreliable over time or from other outside forces. In a simple setting, we model a network as a…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
A $3$-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
The maximum genus $\gamma_M(G)$ of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal…
Reliability is one of the important measures of how well the system meets its design objective, and mathematically is the probability that a system will perform satisfactorily for at least a given period of time. When the system is…
The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its…
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…