Vertex Separation Research Articles

Optimal filter assignment policy against link flooding attack

A Link Flooding (LFA) attack is a special type of Denial-of-Service (DoS) attack in which the attacker sends out a huge number of requests to exhaust the capacity of a link on the path the traffic comes to a server. As a result, user traffic cannot reach the server. As a result, DoS and degradation of Quality-of-Service (QoS) occur. Because the attack traffic does not go to the victim, protecting the legitimate traffic alone is hard for the victim. The victim can protect its legitimate traffic by using a special type of router called filter router (FR). An FR can receive server filters and apply them to block a link incident to it. An FR probabilistically appends its own IP address to packets it forwards, and the victim uses that information to discover the traffic topology. By analyzing traffic rates and paths, the victim identifies some links that may be congested. The victim needs to select some of these possible congested links (PCLs) and send a filter to the corresponding FR so that legitimate traffic avoids congested paths. In this paper, we formulate two optimization problems for blocking the least number of PCLs so that the legitimate traffic goes through a non-congested path. We consider the scenario where every user has at least one non-congested shortest path in the first problem. We extend the first problem to a scenario where there are some users whose shortest paths are all congested. We transform the original problem to the vertex separation problem to find the links to block. We use a custom-built Java multi-threaded simulator and conduct extensive simulations to support our solutions.

Revisiting 2D Convolutional Neural Networks for Graph-Based Applications.

Graph convolutional networks (GCNs) are widely used in graph-based applications such as graph classification and segmentation. However, current GCNs have limitations on implementation such as network architectures due to their irregular inputs. In contrast, convolutional neural networks (CNNs) are capable of extracting rich features from large-scale input data, but they do not support general graph inputs. To bridge the gap between GCNs and CNNs, in this paper we study the problem of how to effectively and efficiently map general graphs to 2D grids that CNNs can be directly applied to, while preserving graph topology as much as possible. We therefore propose two novel graph-to-grid mapping schemes, namely, graph-preserving grid layout (GPGL) and its extension Hierarchical GPGL (H-GPGL) for computational efficiency. We formulate the GPGL problem as integer programming and further propose an approximate yet efficient solver based on a penalized Kamada-Kawai method, a well-known optimization algorithm in 2D graph drawing. We propose a novel vertex separation penalty that encourages graph vertices to lay on the grid without any overlap. Along with this image representation, even extra 2D maxpooling layers contribute to the PointNet, a widely applied point-based neural network. We demonstrate the empirical success of GPGL on general graph classification with small graphs and H-GPGL on 3D point cloud segmentation with large graphs, based on 2D CNNs including VGG16, ResNet50 and multi-scale maxout (MSM) CNN.

Single photoelectron time resolution studies of the PICOSEC-Micromegas detector

Detectors with a time resolution of a few tens of picoseconds and long-term durability in high particle fluxes are necessary for an accurate vertex separation in future particle physics experiments. The PICOSEC-Micromegas detector concept is a Micro-Pattern Gaseous Detector (MPGD) based solution addressing this particular challenge. It is based on a Micromegas detector coupled to a Cherenkov radiator and a photocathode. Primary electrons from the incident particles are generated in the photocathode and the time fluctuations due to different primary ionisation positions in the gaseous volume are reduced. The feasibility to reach a good time resolution using this concept was demonstrated in test beam studies, and time resolution values down to 24 ps were measured with muon beams at the CERN SPS accelerator complex. The previously simulated effects of different detector parameters on the time resolution were confirmed by measurements. For these measurements, a femtosecond laser system is used. For a single photoelectron, a time resolution of better than 50 ps is achieved mostly by minimising the drift gap distance. Furthermore, gain and Amplitude-to-Signal ratio (A/Q) with different gas mixtures are compared.

A branch-and-price algorithm for capacitated hypergraph vertex separation

We exactly solve the $${\mathcal {NP}}$$-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit in preprocessing. We perform an extensive computational study, in particular on hypergraphs coming from the application of re-arranging a matrix into single-bordered block-diagonal form. Our experimental results show that our proposal complements the previous exact approaches in terms of applicability for larger k, and significantly outperforms them in the case $$k=\infty $$.

PICOSEC-Micromegas: Robustness measurements and study of different photocathode materials

Detectors with a time resolution of 20-30 ps and a reliable performance in high particles flux environments are necessary for an accurate vertex separation in future HEP experiments. The PICOSEC-Micromegas detector concept is a Micro-Pattern Gaseous Detector (MPGD) based solution addressing this particular challenge. The PICOSEC-Micromegas concept is based on a Micromegas detector coupled to a Cherenkov radiator and a photocathode. In this detector concept, all primary electrons are initiated in the photocathode and the time jitter fluctuations are reduced. Different resistive anode layers have been tested with the goal of preserving a stable detector operation in a high intensity pion beam. One important characteristic of a gaseous detector in a high flux environment is the ion backflow (IBF). That can cause damage to more fragile photocathode materials like CsI. Various types of photocathode materials have been tested in order to find a robust solution against IBF bombardment.

Robust $H_2$ Control of Linear Systems With Mismatched Quantization

This paper is concerned with the $H_2$ control of linear systems with multiple quantization channels. The quantization parameters of each channel are not required to be identical. The resultant mismatches are represented by polytopic uncertainties. A composite controller composed of linear and nonlinear parts is designed to meet the required $H_2$ performance and offset the quantization error. Resorting to a vertex separation technique and Finsler lemma instead of matrix inverse operations, new synthesis conditions for the desired linear part are derived in terms of linear matrix inequalities, which are further extended to treat systems with norm-bounded uncertainties. A comparison of conservativeness between the proposed methods and the existing ones is demonstrated by two numerical examples.

Search Numbers in Networks with Special Topologies

In this paper, we consider the problem of finding the minimum number of searchers to sweep networks/graphs with special topological structures. Such a number is called the search number. We first study graphs, which contain only one cycle, and present a linear time algorithm to compute the vertex separation and the optimal layout of such graphs; by a linear-time transformation, we can find the search number of this kind of graphs in linear time. We also investigate graphs, in which every vertex lies on at most one cycle and each cycle contains at most three vertices of degree more than two, and we propose a linear time algorithm to compute their search number and optimal search strategy. We prove explicit formulas for the search number of the graphs obtained from complete k-ary trees by replacing vertices by cycles. We also present some results on approximation algorithms.

Linear ordering based MIP formulations for the vertex separation or pathwidth problem

We consider the task to compute the pathwidth of a graph which is known to be equivalent to solving the vertex separation problem. The latter is naturally modeled as a linear ordering problem with respect to the vertices of the graph. Present mixed-integer programs for the vertex separation problem express linear orders using either position or set assignment variables. However, as we show, the lower bound on the pathwidth obtained when solving their linear programming relaxations is zero for any directed graph. This is one reason for their limited utility in solving larger instances to optimality. We then present a new formulation that is based on conventional linear ordering variables and a slightly different perspective on the problem. Its relaxation provably delivers non-zero lower bounds for any graph whose pathwidth is non-zero. Further structural results for and extensions to this formulation are discussed. Finally, an experimental evaluation of three mixed-integer programs, each representing one of the different yet existing modeling approaches, displays their potentials and limitations when used to solve the problem to optimality in practice.

Performance of flapping airfoil propulsion with LBM method and DMD analysis

In this work, the performance of flapping airfoil propulsion at low Reynolds number of Re = 100–400 is studied numerically with the lattice Boltzmann method (LBM). Combined with immersed boundary method (IBM), the LBM has been widely used to simulate moving boundary problems. The influences of the reduced frequency on the plunging and pitching airfoil are explored. It is found that the leading-edge vertex separation and inverted wake structures are two main coherent structures, which dominate the flapping airfoil propulsion. However, the two structures play different roles in the flow and the combination effects on the propulsion need to be clarified. To do so, we adopt the dynamic mode decomposition (DMD) algorithm to reveal the underlying physics. The DMD has been proven to be very suitable for analyzing the complex transient systems like the vortex structure of flapping flight.

Event-triggered nonfragile [formula omitted] filtering of Markov jump systems with imperfect transmissions

This paper is concerned with the event-triggered nonfragile H∞ filtering of Markov jump systems with interval variations. Integrating the sampler failure into the filter design, two independent random variables satisfying the Bernoulli distribution are utilized to describe the imperfect transmissions from sensor to event generator and event generator to filter, respectively. The resultant event-triggered scheme is represented by a stochastic form. With the help of stochastic analysis technique, sufficient conditions for the filtering error system to be stochastically stable with the required H∞ performance are formulated in terms of linear matrix inequalities. A structured vertex separation method is adopted to handle filter gains with interval variations. The validity of the proposed approach is verified by an RLC circuit.

Polynomial Time Efficient Construction Heuristics for Vertex Separation Minimization Problem

Vertex Separation Minimization Problem (VSMP) consists of finding a layout of a graph G = (V, E) which minimizes the maximum vertex cut or separation of a layout. It is an NP-complete problem in general for which metaheuristic techniques can be applied to find near optimal solution. VSMP has applications in VLSI design, graph drawing and computer language compiler design. VSMP is polynomially solvable for grids, trees, permutation graphs and cographs. Construction heuristics play a very important role in the metaheuristic techniques as they are responsible for generating initial solutions which lead to fast convergence. In this paper, we have proposed three construction heuristics H1, H2 and H3 and performed experiments on Grids, Small graphs, Trees and Harwell Boeing graphs, totaling 248 instances of graphs. Experiments reveal that H1, H2 and H3 are able to achieve best results for 88.71%, 43.5% and 37.1% of the total instances respectively while the best construction heuristic in the literature achieves the best solution for 39.9% of the total instances. We have also compared the results with the state-of-the-art meta-heuristic GVNS and observed that the proposed construction heuristics improves the results for some of the input instances. It was found that GVNS obtained best results for 82.9% instances of all input instances and the heuristic H1 obtained best results for 82.3% of all input instances.

Performance of algorithms that reconstruct missing transverse momentum in sqrt{s}= 8 TeV proton\u2013proton collisions in the ATLAS detector

The reconstruction and calibration algorithms used to calculate missing transverse momentum (E_{text {T}}^{text {miss}} ) with the ATLAS detector exploit energy deposits in the calorimeter and tracks reconstructed in the inner detector as well as the muon spectrometer. Various strategies are used to suppress effects arising from additional proton–proton interactions, called pileup, concurrent with the hard-scatter processes. Tracking information is used to distinguish contributions from the pileup interactions using their vertex separation along the beam axis. The performance of the E_{text {T}}^{text {miss}} reconstruction algorithms, especially with respect to the amount of pileup, is evaluated using data collected in proton–proton collisions at a centre-of-mass energy of 8 text {TeV} during 2012, and results are shown for a data sample corresponding to an integrated luminosity of 20.3, mathrm{fb}^{-1}. The simulation and modelling of E_{text {T}}^{text {miss}} in events containing a Z boson decaying to two charged leptons (electrons or muons) or a W boson decaying to a charged lepton and a neutrino are compared to data. The acceptance for different event topologies, with and without high transverse momentum neutrinos, is shown for a range of threshold criteria for E_{text {T}}^{text {miss}} , and estimates of the systematic uncertainties in the E_{text {T}}^{text {miss}} measurements are presented.

A quality and distance guided metaheuristic algorithm for vertex separation problem

This paper presents a quality and distance guided metaheuristic algorithm (QD-ILS) for solving the vertex separation problem. QD-ILS integrates a basic local search procedure with QD-LS strategy, which uses an augmented evaluation function that considers both solution quality and distance between the current solution and the best found solution to guide the search to explore promising regions of the search space. Assessed on two sets of 162 common benchmark instances, QD-ILS achieves highly competitive results in terms of both solution quality and computational efficiency compared with the state-of-the-art algorithms in the literature. Specifically, it improves the previous best known results for 33 out of 162 benchmark instances and matches the best known results on all except four of the remaining instances compared with the state-of-the-art algorithms in the literature. The impact of the distance and quality-based diversification strategy is also investigated.

A tracking system to calculate patient skin dose in real-time during neurointerventional procedures using a biplane x-ray imaging system.

Neurovascular interventional procedures using biplane fluoroscopic imaging systems can lead to increased risk of radiation-induced skin injuries. The authors developed a biplane dose tracking system (Biplane-DTS) to calculate the cumulative skin dose distribution from the frontal and lateral x-ray tubes and display it in real-time as a color-coded map on a 3D graphic of the patient for immediate feedback to the physician. The agreement of the calculated values with the dose measured on phantoms was evaluated. The Biplane-DTS consists of multiple components including 3D graphic models of the imaging system and patient, an interactive graphical user interface, a data acquisition module to collect geometry and exposure parameters, the computer graphics processing unit, and functions for determining which parts of the patient graphic skin surface are within the beam and for calculating dose. The dose is calculated to individual points on the patient graphic using premeasured calibration files of entrance skin dose per mAs including backscatter; corrections are applied for field area, distance from the focal spot and patient table and pad attenuation when appropriate. The agreement of the calculated patient skin dose and its spatial distribution with measured values was evaluated in 2D and 3D for simulated procedure conditions using a PMMA block phantom and an SK-150 head phantom, respectively. Dose values calculated by the Biplane-DTS were compared to the measurements made on the phantom surface with radiochromic film and a calibrated ionization chamber, which was also used to calibrate the DTS. The agreement with measurements was specifically evaluated with variation in kVp, gantry angle, and field size. The dose tracking system that was developed is able to acquire data from the two x-ray gantries on a biplane imaging system and calculate the skin dose for each exposure pulse to those vertices of a patient graphic that are determined to be in the beam. The calculations are done in real-time with a typical graphic update time of 30 ms and an average vertex separation of 3 mm. With appropriate corrections applied, the Biplane-DTS was able to determine the entrance dose within 6% and the spatial distribution of the dose within 4% compared to the measurements with the ionization chamber and film for the SK150 head phantom. The cumulative dose for overlapping fields from both gantries showed similar agreement. The Biplane-DTS can provide a good estimate of the peak skin dose and cumulative skin dose distribution during biplane neurointerventional procedures. Real-time display of this information should help the physician manage patient dose to reduce the risk of radiation-induced skin injuries.

Linear Rank-Width of Distance-Hereditary Graphs I. A Polynomial-Time Algorithm

Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid path-width. In this paper, we show that the linear rank-width of every n-vertex distance-hereditary graph, equivalently a graph of rank-width at most 1, can be computed in time $${\mathcal {O}}(n^2\cdot \log _2 n)$$O(n2·log2n), and a linear layout witnessing the linear rank-width can be computed with the same time complexity. As a corollary, we show that the path-width of every n-element matroid of branch-width at most 2 can be computed in time $${\mathcal {O}}(n^2\cdot \log _2 n)$$O(n2·log2n), provided that the matroid is given by its binary representation. To establish this result, we present a characterization of the linear rank-width of distance-hereditary graphs in terms of their canonical split decompositions. This characterization is similar to the known characterization of the path-width of forests given by Ellis, Sudborough, and Turner [The vertex separation and search number of a graph. Inf. Comput., 113(1):50---79, 1994]. However, different from forests, it is non-trivial to relate substructures of the canonical split decomposition of a graph with some substructures of the given graph. We introduce a notion of `limbs' of canonical split decompositions, which correspond to certain vertex-minors of the original graph, for the right characterization.

DAG representation of asymmetric independence models arising in coherent conditional possibility theory

In this paper we study the representation by means of an acyclic directed graph (DAG) of the independence model induced by a coherent T-conditional possibility (where T stands for the minimum or a strict t-norm). Such models are in general not closed under symmetric property, so we must rely on a proper asymmetric notion of vertex separation which produces structures closed under all graphoid properties and their reverses except for symmetry (namely, asymmetric graphoids). Focusing on this kind of models we present an efficient procedure to generate and represent them symbolically. We then introduce asymmetric Markov properties and prove their equivalence, providing in this way a method to extract the model encoded in a DAG. Finally, an algorithm to build a minimal I-map, given an ordering of the random variables, is drawn.

Combining intensification and diversification strategies in VNS. An application to the Vertex Separation problem

The Vertex Separation problem (VSP) is an NP-hard problem with practical applications in VLSI design, graph drawing and computer language compiler design. VSP belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. In this paper, we propose different heuristic methods and embed them into a Variable Neighborhood Search scheme to solve this problem. More precisely, we propose (i) a constructive algorithm, (ii) four shake procedures, (iii) two neighborhood structures, (iv) efficient algorithmic strategies to explore them, (v) an extended version of the objective function to facilitate the search process and finally, (vi) we embed these strategies in a Reduced Variable Neighborhood Search (RVNS), a Variable Neighborhood Descent (VND) and a General Variable Neighborhood Search (GVNS). Additionally, we provide an extensive experimental comparison among them and with the best previous method of the literature. We consider three different benchmarks, totalizing 162 representative instances. The experimentation reveals that our best procedure (GVNS) improves the state of the art in both quality and computing time. This fact is confirmed by non-parametric statistical tests. In addition, when considering only the largest instances, the other two proposed variants (RVNS and VND) also obtain statistically significant differences with respect to the best previous method identified in the state of the art.

An experimental comparison of Variable Neighborhood Search variants for the minimization of the vertex-cut in layout problems

Variable Neighborhood Search (VNS) is a metaheuristic for solving optimization problems based on a systematic change of neighborhoods. In recent years, a large variety of VNS strategies have been proposed. However, we have only found limited experimental comparisons among different VNS variants. This paper reviews three VNS strategies for finding near-optimal solutions for vertex-cut minimization problems. Specifically, we consider the min-max variant (Vertex Separation Problem) and the min-sum variant (SumCut Minimization Problem). We also present an preliminary computational comparison of the methods on previously reported instances.

Radiation damage in the LHCb VELO

The VErtex LOcator (VELO) is a silicon strip detector designed to reconstruct particle tracks and vertices produced by proton–proton interactions near to the LHCb interaction point. The excellent track resolution and decay vertex separation provided by the VELO are essential to all LHCb analyses. For the integrated luminosity delivered by the LHC up to the end of 2011 the VELO is exposed to higher particle fluences than any other silicon detector of the four major LHC experiments. These proceedings present results from radiation damage studies carried out during the first two years of data taking at the LHC. Radiation damage has been observed in all of the 88 VELO silicon strip sensors, with many sensors showing evidence of type-inversion in the highest fluence regions. Particular attention has been given to the two n+-on-p sensors as this type of sensor is one of the leading candidates for the LHC silicon detector upgrades.

Variable neighborhood search for the Vertex Separation Problem

The Vertex Separation Problem belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. This optimization problem is strongly related to other well-known graph problems; such as the Path-Width, the Node Search Number or the Interval Thickness, among others. All of these optimization problems are NP-hard and have practical applications in VLSI (Very Large Scale Integration), computer language compiler design or graph drawing. Up to know, they have been generally tackled with exact approaches, presenting polynomial-time algorithms to obtain the optimal solution for specific types of graphs. However, in spite of their practical applications, these problems have been ignored from a heuristic perspective, as far as we know. In this paper we propose a pure 0-1 optimization model and a metaheuristic algorithm based on the variable neighborhood search methodology for the Vertex Separation Problem on general graphs. Computational results show that small instances can be optimally solved with this optimization model and the proposed metaheuristic is able to find high-quality solutions with a moderate computing time for large-scale instances.