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The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
In order to detect unknown intrusions and runtime errors of computer programs, the cyber-security community has developed various detection techniques. Anomaly detection is an approach that is designed to profile the normal runtime behavior…
Graph modification problems, which aim to find a small set of modifications to a graph so that it satisfies a desired property, have been studied for several special graph classes. The literature is rather rich in NP-completeness results…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
We propose a new defense mechanism against undetected infiltration into controllers in cyber-physical systems. To this end, we cautiously design the outputs of the sensors that monitor the state of the system. Different from the defense…
Protecting sensitive program content is a critical issue in various situations, ranging from legitimate use cases to unethical contexts. Obfuscation is one of the most used techniques to ensure such protection. Consequently, attackers must…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
For any graph~\(G,\) a set of vertices~\({\cal V}\) is said to be dominating if every vertex of~\(G\) contains at least one node of~\(G\) and separating if each vertex~\(v\) contains a unique neighbour~\(u_v \in {\cal V}\) that is adjacent…
We introduce a new graph-theoretic concept in the area of network monitoring. A set $M$ of vertices of a graph $G$ is a \emph{distance-edge-monitoring set} if for every edge $e$ of $G$, there is a vertex $x$ of $M$ and a vertex $y$ of $G$…
We study verification (decision) problems for graph properties in distributed networks under the locally checkable labeling framework, where nodes use labels (proofs) and local neighborhoods to decide acceptance or rejection. Our focus is…
Let $G$ be a connected graph on $n$ vertices and $C$ be an $(n,k,d)$ code with $d\ge 2$, defined on the alphabet set $\{0,1\}^m$. Suppose that for $1\le i\le n$, the $i$-th vertex of $G$ holds an input symbol $x_i\in\{0,1\}^m$ and let…
In the literature, several identification problems in graphs have been studied, of which, the most widely studied are the ones based on dominating sets as a tool of identification. Hereby, the objective is to separate any two vertices of a…
The growing complexity of modern Cyber-Physical Systems (CPS) and the frequent communication between their components make them vulnerable to malicious attacks. As a result, secure state estimation is a critical requirement for the control…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
We investigate the problem of distributed sensors' failure detection in networks with a small number of defective sensors, whose measurements differ significantly from neighboring sensor measurements. Defective sensors are represented by…
The goal of an Intrusion Detection is inadequate to detect errors and unusual activity on a network or on the hosts belonging to a local network by monitoring network activity. Algorithms for building detection models are broadly classified…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…