Related papers: On Fault Tolerant Feedback Vertex Set
Reliability has taken centre stage in the development of high-performance computing processors. A Surge of interest is noticeable in recent times in formulating fault and failure models, understanding failure mechanism and strategizing…
In this paper, we develop a new parameterized algorithm for the {\sc Independent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, the goal of the problem is to determine whether there exists a vertex subset $F\subseteq V$ such…
Previous research on selective protection for neural network components typically exploits only static vulnerability differences. Although these methods improve upon classical modular redundancy, they still incur substantial overhead for…
In a standard $f$-connectivity network design problem, we are given an undirected graph $G=(V,E)$, a cut-requirement function $f:2^V \rightarrow {\mathbb{N}}$, and non-negative costs $c(e)$ for all $e \in E$. We are then asked to find a…
An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these…
The structures for the expression of fault-tolerance provisions into the application software are the central topic of this dissertation. Structuring techniques provide means to control complexity, the latter being a relevant factor for the…
In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph $G=(V,E)$, consisting of a vertex set $V$ of size $n$ and an edge set $E$. Each vertex in $V$ is assigned a color from the set…
We consider the Sparse Hitting Set (Sparse-HS) problem, where we are given a set system $(V,\mathcal{F},\mathcal{B})$ with two families $\mathcal{F},\mathcal{B}$ of subsets of $V$. The task is to find a hitting set for $\mathcal{F}$ that…
Application partitioning and code offloading are being researched extensively during the past few years. Several frameworks for code offloading have been proposed. However, fewer works attempted to address issues occurred with its…
In the classical \emph{survivable-network-design problem} (SNDP), we are given an undirected graph $G = (V, E)$, non-negative edge costs, and some $(s_i,t_i,r_i)$ tuples, where $s_i,t_i\in V$ and $r_i\in\mathbb{Z}_+$. We seek a minimum-cost…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
Convolutional neural networks (CNNs) are becoming more and more important for solving challenging and critical problems in many fields. CNN inference applications have been deployed in safety-critical systems, which may suffer from soft…
We study the fault-tolerance of networks from both the structural and computational point of view using the minimum leaf number of the corresponding graph $G$, i.e. the minimum number of leaves of the spanning trees of $G$, and its…
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
In three dimensional integrated circuits (3D-ICs), through silicon via (TSV) is a critical technique in providing vertical connections. However, the yield and reliability is one of the key obstacles to adopt the TSV based 3D-ICs technology…
We give a short and easy upper bound on the worst-case size of fault tolerant spanners, which improves on all prior work and is fully optimal at least in the setting of vertex faults.
For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on…
Fault Trees represent an essential tool in the reliability and risk assessment of engineering systems. By decomposing the structure of the system into Boolean function, Fault Trees allow the quantitative and qualitative analysis of the…
Fault tolerance in multi-core architecture has attracted attention of research community for the past 20 years. Rapid improvements in the CMOS technology resulted in exponential growth of transistor density. It resulted in increased…