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We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…
A set S of vertices of a graph G is a dominating set of G if every vertex u of G is either in S or it has a neighbour in S. In other words, S is dominating if the sets S\cap N[u] where u \in V(G) and N[u] denotes the closed neighbourhood of…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
This study explores the effectiveness of graph neural networks (GNNs) for vulnerability detection in software code, utilizing a real-world dataset of Java vulnerability-fixing commits. The dataset's structure, based on the number of…
For autonomous driving, an essential task is to detect surrounding objects accurately. To this end, most existing systems use optical devices, including cameras and light detection and ranging (LiDAR) sensors, to collect environment data in…
Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the tracking paths problem is that of finding the smallest subset of vertices in $G$ whose intersection with any $s$-$t$ path results in a unique sequence. This problem is…
Modern compilers leverage block coverage profile data to carry out downstream profile-guided optimizations to improve the runtime performance and the size of a binary. Given a control-flow graph $G=(V, E)$ of a function in the binary, where…
In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph $G$ such that from the labels of any three vertices $u,v,f$ we can infer the $u$-to-$v$ distance in the graph $G\setminus \{f\}$. We show that any…
In large-scale networks, communication links between nodes are easily injected with false data by adversaries. This paper proposes a novel security defense strategy from the perspective of attack detection scheduling to ensure the security…
Fault injection attacks deliberately inject faults into a device via physical channels to disturb its regular execution. Adversaries can effectively deduce secrets by analyzing both the normal and faulty outputs, posing serious threats to…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
Network intrusion detection sensors are usually built around low level models of network traffic. This means that their output is of a similarly low level and as a consequence, is difficult to analyze. Intrusion alert correlation is the…
To perform any meaningful optimization task, power distribution operators need to know the topology and line impedances of their electric networks. Nevertheless, distribution grids currently lack a comprehensive metering infrastructure.…
Identifying vulnerable code is a precautionary measure to counter software security breaches. Tedious expert effort has been spent to build static analyzers, yet insecure patterns are barely fully enumerated. This work explores a deep…
Hacking and false data injection from adversaries can threaten power grids' everyday operations and cause significant economic loss. Anomaly detection in power grids aims to detect and discriminate anomalies caused by cyber attacks against…
The minimum completion (fill-in) problem is defined as follows: Given a graph family $\mathcal{F}$ (more generally, a property $\Pi$) and a graph $G$, the completion problem asks for the minimum number of non-edges needed to be added to $G$…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
A resolving set for a simple graph $G$ is a subset of vertex set of $G$ such that it distinguishes all vertices of $G$ using the shortest distance from this subset. This subset is a metric basis if it is the smallest set with this property.…
Motivated by increasing penetration of distributed generators (DGs) and fast development of micro-phasor measurement units ({\mu}PMUs), this paper proposes a novel graph-based faulted line identification algorithm using a limited number of…
We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two…