Related papers: A Note on the Computational Complexity of Unsmooth…
Large, complex networks are ubiquitous in nature and society, and there is great interest in developing rigorous, scalable methods for identifying and characterizing their vulnerabilities. This paper presents an approach for analyzing the…
Let G be a graph with minimum degree $\delta$. It is well-known that maximal adjacency orderings (MAOs) compute a vertex set S such that every pair of S is connected by at least $\delta$ internally vertex-disjoint paths in G. We present an…
The spreading of dangerous malware or faults in inter-dependent networks of electronics devices has raised deep concern, because from the ICT networks infections may propagate to other Critical Infrastructures producing the well-known…
In a connected simple graph G = (V(G),E(G)), each vertex is assigned one of c colors, where V(G) can be written as a union of a total of c subsets V_{1},...,V_{c} and V_{i} denotes the set of vertices of color i. A subset S of V(G) is…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
Viewpoint invariance remains challenging for visual recognition in the 3D world, as altering the viewing directions can significantly impact predictions for the same object. While substantial efforts have been dedicated to making neural…
Adversarial training (AT) is proved to reliably improve network's robustness against adversarial data. However, current AT with a pre-specified perturbation budget has limitations in learning a robust network. Firstly, applying a…
It is commonly believed that networks cannot be both accurate and robust, that gaining robustness means losing accuracy. It is also generally believed that, unless making networks larger, network architectural elements would otherwise…
We consider the ``minimum degree spanning tree'' problem. As input, we receive an undirected, connected graph $G=(V, E)$ with $n$ nodes and $m$ edges, and our task is to find a spanning tree $T$ of $G$ that minimizes $\max_{u \in V}…
Adversarial training (AT) is a simple yet effective defense against adversarial attacks to image classification systems, which is based on augmenting the training set with attacks that maximize the loss. However, the effectiveness of AT as…
Power electronics systems are increasingly exposed to cyber threats due to their integration with digital controllers and communication networks. However, an attacker-oriented metric is still lacking to quantify the extent to which a node…
Visual Document Understanding (VDU) systems have achieved strong performance in information extraction by integrating textual, layout, and visual signals. However, their robustness under realistic adversarial perturbations remains…
Since the advent of Spectre attacks, researchers and practitioners have developed a range of hardware and software measures to counter transient execution attacks. A prime example of such mitigation is speculative load hardening in LLVM,…
Let $G=(V,E)$ be a graph with unit-length edges and nonnegative costs assigned to its vertices. Being given a list of pairwise different vertices $S=(s_1,s_2,\ldots,s_p)$, the {\em prioritized Voronoi diagram} of $G$ with respect to $S$ is…
The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper,…
This note concerns the trade-off between the degree of the constraint graph and the gap in hardness of approximating the Min-Rep variant of Label Cover (aka Projection Game). We make a very simple observation that, for NP-hardness with gap…
The vertex PI index is a distance--based molecular structure descriptor, that recently found numerous chemical applications. In order to increase diversity of this topological index for bipartite graphs, we introduce weighted version…
Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…
Recent studies demonstrate that Graph Neural Networks (GNNs) are vulnerable to slight but adversarially designed perturbations, known as adversarial examples. To address this issue, robust training methods against adversarial examples have…
Given a graph $G$ and a subset of vertices $S = \{w_1, \ldots, w_t\} \subseteq V(G)$, the multiset representation of a vertex $u\in V(G)$ with respect to $S$ is the multiset $m(u|S) = \{| d_G(u, w_1), \ldots, d_G(u, w_t) |\}$. A subset of…