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(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost)…
The focus of this work is on Statistical Process Control (SPC) of a manufacturing process based on available measurements. Two important applications of SPC in industrial settings are fault detection and diagnosis (FDD). In this work a deep…
Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in…
The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading…
We give a fully polynomial-time randomized approximation scheme (FPRAS) for the all-terminal network reliability problem, which is to determine the probability that, in a undirected graph, assuming each edge fails independently, the…
We identify the asymptotic probability of a configuration model $\mathrm{CM}_n(\boldsymbol{d})$ to produce a connected graph within its critical window for connectivity that is identified by the number of vertices of degree 1 and 2, as well…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components…
The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations,…
Financial networks model a set of financial institutions (firms) interconnected by obligations. Recent work has introduced to this model a class of obligations called credit default swaps, a certain kind of financial derivatives. The main…
We consider the problem of computing sample points in each connected component of a semi-algebraic set defined by the non-vanishing or the positivity of an n-variate polynomial of degree d, with rational coefficients of bit size bounded by…
The Graph Minors Series of Robertson and Seymour forms the foundation of algorithmic structural graph theory, yielding fixed-parameter algorithms for problems such as Disjoint Paths, Rooted Minor Checking, and Folio. A key ingredient behind…
The \emph{$f$-fault-tolerant connectivity labeling} ($f$-FTC labeling) is a scheme of assigning each vertex and edge with a small-size label such that one can determine the connectivity of two vertices $s$ and $t$ under the presence of at…
The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…
It is well known that when $f(v)$ is a constant for each vertex $v$, the connected $f$-factor problem is NP-Complete. In this note we consider the case when $f(v) \geq \lceil \frac{n}{2.5}\rceil$ for each vertex $v$, where $n$ is the number…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
We give a simple, local process for nodes in an undirected graph to form non-adjacent clusters that (1) have at most a polylogarithmic diameter and (2) contain at least half of all vertices. Efficient deterministic distributed clustering…
The simplest null models for networks, used to distinguish significant features of a particular network from {\it a priori} expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These…
A (control) network over a finite ring is proposed. Using semi-tensor product (STP) of matrices, a set of algebraic equations are provided to verify whether a finite set with two binary operators is a ring. It is then shown that the…
Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of…