Time Complexity Research Articles

A Review Paper on Memory Fault Models and its Algorithms

The significance of testing semiconductor memories has grown significantly in the semiconductor industry due to the increased density of modern memory chips. This paper aims to investigate and analyze different types of functional faults present in today's memory technology. These faults include stuck-at faults, transition faults, coupling faults, address decoder faults, and neighborhood pattern-sensitive faults. The paper also delves into the techniques utilized to identify and detect these faults. In particular, the focus is placed on the importance of zero-one, checkerboard, and March pattern tests, which are widely employed to assess functional memory defects at different levels, such as the chip level, array level, and board level. Furthermore, the study provides an in-depth exploration of various test algorithms and thoroughly examines their fault coverage capabilities. Overall, this review paper provides valuable insights into the challenges posed by the dense nature of modern memory chips and offers a comprehensive analysis of functional faults in memory technology. By emphasizing the importance of testing and presenting a detailed exploration of fault detection methods and test algorithms, this study contributes to the advancement of reliable and high-performance memory devices in the electronic industry suggesting that MARCH algorithms outperform others when considering factors like fault coverage, power efficiency, area optimization, and time complexity parameters, making them the preferable choice for reliable and high-performance memory devices in the electronic industry.

Perfect Resolution of Strong Conflict-Free Colouring of Interval Hypergraphs

The \(k\) -Strong Conflict-Free ( \(k\) -SCF, in short) colouring problem seeks to find a colouring of the vertices of a hypergraph \(H\) using minimum number of colours so that in every hyperedge \(e\) of \(H\) , there are at least \(\min\{|e|,k\}\) vertices whose colours are different from that of all other vertices in \(e\) . In the case of interval hypergraphs, we present an exact \({\mathsf{P}}\) -time algorithm for the \(k\) -SCF problem thus solving an open problem posed by Cheilaris et al. (2014). We achieve our results by showing that for any hypergraph, a \(k\) -SCF colouring is a proper colouring of a related simple graph which we refer to as a co-occurrence graph . We then show that a co-occurrence graph is obtained by identifying an induced subgraph of a second simple graph that we introduce, which we refer to as the conflict graph . For interval hypergraphs, we show that each co-occurrence graph and the conflict graph are perfect graphs. This property plays a crucial role in our polynomial time algorithm. Secondly, we show that for an interval hypergraph, the \(1\) -SCF colouring number is the minimum partition of its intervals into sets such that each set has an exact hitting set (a hitting set in which each interval is hit exactly once).

Blind image authentication using singular value decomposition with enhanced robustness by augmenting hamming code

Singular value decomposition (SVD) based image authentication has widespread applications for digital media protection including forensic and medical domains due to the high stability and robustness of singular values under small perturbations. However, most of these techniques are non-blind and have high redundancies for the extraction of secret data. The proposed scheme employs a blind extraction strategy by utilizing the intrinsic relationship of coefficient pairs of the U matrix of the host image blocks. This relationship is utilized to hide a secret binary bit after computing a threshold value in constant time. The host image underwent block-wise decomposition and hash-based randomization of blocks, followed by block-wise SVD for embedding secret bits in the U matrix. Hamming coded watermark is embedded for high precision extraction under active attacks. High imperceptibility and strong robustness are observed under attacks when tested across general purpose as well as image datasets and the system outperforms many existing works. Experimental observation shows the average PSNR between the host and marked image and average NCC between embedded and extracted watermark to be 36.98 dB and 0.999 respectively for the SIPI dataset whereas 52.7 dB and 1 respectively for the X-Ray dataset. The system exhibited high robustness under Salt-and-pepper noise (SAPN), Gaussian Noise (GAUN), Cropping (CRP), Median Filtering (MF), Histogram Equalization (HEQ), and Jpeg Compression (JPC) with average NCC values of 0.998, 1, 0.932, 0.999 and 0.967 respectively for X-Ray dataset. The time complexity O (M × N) is observed for both embedding and extraction algorithms for a host image of size M × N.

Prediction of permeability characteristics of mine slurries and sediments using finite-strain framework by optimisation algorithms

Determining the permeability characteristics of mine tailing slurries through laboratory finite-strain consolidation tests is costly due to the extensive testing required. An alternative approach involves back-predicting hydraulic conductivities from settling column test data. This study employed settlement and excess pore pressure data as inputs in optimising the permeability parameters using the finite-strain consolidation (FSC) framework. The proposed approach used the finite difference method to solve the governing equation for FSC in the forward analysis. Two novel variants of the Artificial Bee Colony (ABC) algorithm, namely the Modified Artificial Bee Colony (MABC) and the Hybrid Artificial Bee Colony (HABC) algorithms, were used to back-predict the hydraulic conductivity function parameters from the FSC test data. These models predicted the permeability characteristics using the temporal variation of the settlements for six slurries and excess pore pressure dissipation data for four slurries. The performance of the proposed algorithms along with Hybrid Particle Swarm Optimisation (HPSO) was compared with the conventional optimisation algorithms, viz., PSO, ABC, and Quantum PSO (QPSO). The HABC and HPSO exhibited remarkable stability, consistently converging to identical solution sets across multiple iterations, thereby outperforming other algorithms in this study. Despite its higher time complexity by HABC relative to the other evaluated methods, this complexity is warranted for enhanced robustness. The current study is helpful in brining practical and reliable methodologies for estimating the hydraulic conductivity function from field-scale conductivity (FSC) data, providing critical insights for the safe and efficient management of slurry wastes.

Randomized SearchRank: A semiclassical approach to a quantum search engine

The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the N/M ratio between the network size N and the number of marked nodes M is sufficiently large. We propose a modification of the algorithm, replacing the underlying Szegedy quantum walk with a semiclassical walk. To maintain the same time complexity as the quantum SearchRank algorithm we propose a simplification of the algorithm. This new algorithm is called randomized SearchRank, since it corresponds to a quantum walk over a randomized mixed state. The performance of the SearchRank algorithms is first analyzed on an example network and then statistically on a set of different networks of increasing size and different number of marked nodes. On the one hand, to test the search ability of the algorithms, it is computed how the probability of measuring the marked nodes decreases with N/M for the quantum SearchRank, but remarkably it remains at a high value around 0.9 for our semiclassical algorithms, solving the quantum SearchRank problem. The time complexity of the algorithms is also analyzed, obtaining a quadratic speedup with respect to the classical ones. On the other hand, the ranking functionality of the algorithms has been investigated, obtaining a good agreement with the classical PageRank distribution. Finally, the dependence of these algorithms on the intrinsic PageRank damping parameter has been clarified. Our results suggest that this parameter should be below a threshold so that the execution time does not increase drastically. Published by the American Physical Society 2024

Single-molecule tracking reveals dynamic regulation of ribosomal scanning.

How eukaryotic ribosomes traverse messenger RNA (mRNA) leader sequences to search for protein-synthesis start sites remains one of the most mysterious aspects of translation and its regulation. While the search process is conventionally described by a linear "scanning" model, its exquisitely dynamic nature has restricted detailed mechanistic study. Here, we observed single Saccharomyces cerevisiae ribosomal scanning complexes in real time, finding that they scan diverse mRNA leaders at a rate of 10 to 20 nt s-1. We show that specific binding of a protein to its mRNA leader sequence substantially arrests scanning. Conversely, impairing scanning-complex guanosine 5'-triphosphate hydrolysis results in native start-site bypass. Our results illustrate an mRNA-centric, kinetically controlled regulatory model where the ribosomal pre-initiation complex amplifies a nuanced energetic landscape to regulate scanning and start-site selection fidelity.

Stochastic weighted particle control for electrostatic particle-in-cell Monte Carlo collision simulations in an axisymmetric coordinate system

The non-uniform grids in the axisymmetric coordinate system pose a significant challenge for electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) simulations because they require numerous macroparticles to manage numerical heating around the mid-axis. To address this, we have developed a stochastic weighted particle control method that selectively samples small-weight particles, effectively controlling the particle number without inducing numerical heating. This method is based on a rejection-acceptance probability merging scheme, which is easy to implement and has a low time complexity. We have also made essential modifications, including a corrected density deposition scheme, an energy conservation scheme, and the introduction of target weights. By applying this particle control method, the number of macroparticles in the simulation can be reduced by more than one order of magnitude, significantly reducing the required computing time and storage. Furthermore, appropriately setting target weights also enables enhanced resolution of dilute regions with an acceptable increase in computational cost.

Computational quest, synthesis and anticancer profiling of 3-methyl quinoxaline-2-one-based active hits against the tyrosine kinase

BackgroundCancer is the predominant cause of mortality and a remarkable obstacle to elevating life anticipation in every nation on globe. Hepatocellular carcinoma (HCC), a hyper-vascular tumour, develops and progresses due to angiogenesis, a key feature of malignancy. HCC exhibits high neoangiogenic activity because of the need to generate new blood vessels for tumour growth.MethodsThe present work includes the construction of virtual library of ligands, virtual screening using the Dockthor-VS server, ADMET study using the SwissADME and Osiris property explorer. All the synthesized compounds were characterized by UV, IR, NMR and mass spectroscopic techniques. MTT assay was done to find the IC50 of the synthesized compounds against HepG2 cell line. The more active compound found is subjected to the molecular dynamics simulation study.ResultsThe ligands exhibited good docking scores, ADMET profile compared to the reference drugs. The target compounds were obtained with the satisfactory yields of 66–82%. The best activity against the HepG2 cancer cell line is observed with the compound SA-4 with IUPAC name (2-(3-methyl-2-oxoquinoxalin-1(2H)-yl)-N-(5-(3-nitrophenyl)-5H-thiazolo[4,3-b] [1,3,4] thiadiazol-2-yl) acetamide). The experimental results obtained show correlation with the in silico results. MD simulation of the compound SA-4 indicates the moderate stability of the protein-ligand complex in real time environment.ConclusionThe results obtained suggest that the compound SA-4 has the potential to be a promising anticancer agent effective against the VEGFR-2 and FGFR-4.Graphical abstract

A lightweight visual mamba network for image recognition under resource-limited environments

The Vision Transformers (ViTs) models show great potential in recognition due to their excellent self-attention mechanisms. However, they often need more computational complexity, making achieving high performance in resource-constrained environments challenging. This paper proposes a lightweight visual model (called LightViM) to tackle these challenges, specifically devised for recognition challenges under resource-constrained environments. Considering the imperative of reducing the model’s computational complexity and resource consumption , we propose lightweight local–global feature fusion modules based on Mamba (LGF-Mamba) aimed at integrating spatially detailed local information with globally contextualized features while maintaining lower linear time complexity. In LGF-Mamba, Mamba sub-blocks are first designed to extract global information; then, for the rapid extraction of local features, LocalE module is designed and integrated into LGF-Mamba, exploring more comprehensive feature representation. This mechanism efficiently directs the network to integrate features from different spatial scales, thereby improving the recognition performance in resource-constrained environments. Experimental results indicate that, in comparison to other leading-edge lightweight methods, the proposed procedure simultaneously achieves superior recognition performance and minimal resource consumption.

String editing under pattern constraints

We introduce the novel Nearest Pattern Constrained String (NPCS) problem of finding a minimum set Q of character mutation, insertion, and deletion edit operations sufficient to modify a string x to contain all contiguous substrings in a pattern set P and no contiguous substrings in a forbidden pattern set F. Letting Σ be the alphabet of allowed characters, and letting η and ϒ be the longest string length and sum of all string lengths in P∪F, respectively, we show that NPCS is fixed-parameter tractable in |P| with time complexity O(2|P|⋅ϒ⋅|Σ|⋅(|P|+η)(|x|+1)). Additionally, we consider a generalization of the NPCS problem in which we allow for constraints based on the membership of substrings in regular languages. In particular, we introduce a problem we denote String Editing under Substring in Language Constraints (StrEdit-SILC), where provided a wildcard-free string x∈Σ⁎, a finite set of regular languages R={L1,L2,…}, and a regular language LF, the objective is to find a minimum cost set of mutation, insertion, and deletion edit operations Q that suffice to convert the input string x into a string x′∈Σ⁎, where no substring has membership in LF, and ∀Li∈R, there exists a substring in Li. Here, letting Ψ and ϖ be the sum of all regular expression lengths and longest regular expression length for languages in R∪{LF}, respectively, and letting Cmid∈N be the maximum cost of an edit operation, we show that StrEdit-SILC is fixed-parameter tractable with respect to Ψ, having time complexity O(2Ψ⋅|x|⋅(ϖ⋅|Σ|+Cmid)). However, we also show that StrEdit-SILC is MAX-SNP-hard and otherwise difficult to approximate under stringent constraints.

An improved whale algorithm for real-time boundary processing and its convergence analysis

Abstract To tackle the deficiencies in the whale algorithm, including its weak stability, sluggish convergence rate, and tendency to get trapped in local optima, an adapted whale optimization algorithm has been created, which introduces quasi-opposition learning and a real-time boundary processing mechanism. In the enhanced algorithm, a quasi-opposition learning mechanism is implemented to broaden the search scope and augment the variety of the population during the initial phases of iteration. This approach also helps to guarantee the convergence of the algorithm in the later phases of iteration. The unified boundary processing method of delay concentration is improved to solve the problem that a large amount of convergence damages diversity if a large number of transgressive individuals are unified and centralized. The algorithm flow is given and the asymptotic fitness and the asymptotic global optimal solution are proved. The time complexity is analyzed theoretically. Ultimately, six recognized algorithms were utilized to simulate the CEC 2017 function set across different scales. Findings indicate that the enhanced algorithm significantly boosts convergence rate, optimization precision, and solution robustness, demonstrating strong convergence characteristics.

A Multichannel Convolutional Decoding Network for Graph Classification.

Graph convolutional networks (GCNs) have shown superior performance on graph classification tasks, and their structure can be considered as an encoder-decoder pair. However, most existing methods lack the comprehensive consideration of global and local in decoding, resulting in the loss of global information or ignoring some local information of large graphs. And the commonly used cross-entropy loss is essentially an encoder-decoder global loss, which cannot supervise the training states of the two local components (encoder and decoder). We propose a multichannel convolutional decoding network (MCCD) to solve the above-mentioned problems. MCCD first adopts a multichannel GCN encoder, which has better generalization than a single-channel GCN encoder since different channels can extract graph information from different perspectives. Then, we propose a novel decoder with a global-to-local learning pattern to decode graph information, and this decoder can better extract global and local information. We also introduce a balanced regularization loss to supervise the training states of the encoder and decoder so that they are sufficiently trained. Experiments on standard datasets demonstrate the effectiveness of our MCCD in terms of accuracy, runtime, and computational complexity.

Exploring nonlinear dynamics in brain functionality through phase portraits and fuzzy recurrence plots.

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.

Reliability analysis of IoV-based vehicle monitoring systems subject to cascading probabilistic common cause failures

As an important application of the Internet of Things (IoT), Internet of Vehicles (IoV)-based vehicle monitoring systems (IVMSs), gathering, processing and communicating traffic and vehicle data, are installed in vehicles and deployed to avoid traffic accidents and ensure road safety. In this paper, the reliability of IVMSs subject to cascading probabilistic common cause failures (CPCCFs) is studied where a common cause (CC) may cause multiple system devices to fail probabilistically and the failures of some devices may further trigger failures of other system devices in a domino manner. Two combinatorial methods are proposed to handle complex cascading effects of directed acyclic graph structure and Hamilton loop structure, respectively. The proposed methods are applicable to any arbitrary time-to-failure distribution of devices and both external and internal CCs are considered. The applications and advantages of the proposed methods are illustrated through an IVMS example. The correctness of the methods is proved by Monte Carlo simulation. The time and space complexity of the methods is also analyzed.

Solving Max-cut Problem with a mixed penalization method for Semidefinite Programming

This paper is an attempt to exploit the opportunity of Semi Definite Programming (SDP), which is an area of convex and conic optimization. Indeed, Numerous NP-hard problems can be solveby using this approach. Hence, we intend to investigate the strength of SDP to model and provide tight relaxations of combinatorial and quadratic problems in order to present a new polynomial time algorithm for solving this robust model. This algorithm was firstly use to solve the nonlinear programs, the reason for which we search to extend it to the SDP programs. Actually, this algorithm designs the combination of two penalization methods. The first one is a primal-dual interior point (PDIM) method while the second one is a primal-dual exterior point (PDEM) method. Unlike the first method, which converges globally, the second one, also called the primal dual nonlinear rescaling method, has local super linear/quadratic convergence. Therefore, it seems appropriate to use a mixed algorithm based on the interior-exterior point method (IEPM). In fact, this resolution starts from the interior method, and at a certain level of execution, it proceeds to exterior method. Hence, a convergence evaluation function is use to know the level of permutation. Through evaluation, it has been approve that our approach is use to solve some instances of max-cut problem. This problem is a central graph theory model that occurs in many real problems and it is one of many NP-hard problems, which has attracted many researchers over the years. Then, we have used a semi definite programming solver SDPA (Semi Definite Programming Algorithm) that is modify to include the exterior point method subroutine. From the computational performance, we conclude that as the problem size increases, interior-exterior point algorithm gets relatively faster. The numerical results obtained are promising.

Injective coloring of subclasses of chordal graphs

An injective k-coloring of a graph G=(V,E) is a function f:V→{1,2,…,k} such that for every pair of vertices u and v having a common neighbor, f(u)≠f(v). The injective chromatic number χi(G) of a graph G is the minimum k for which G admits an injective k-coloring. Given a graph G and a positive integer k, Decide Injective Coloring Problem is to decide whether G admits an injective k-coloring. Decide Injective Coloring Problem is known to be NP-complete for chordal graphs. In this paper, we strengthen this result by proving that Decide Injective coloring Problem remains NP-complete for undirected path graphs, a proper subclass of chordal graphs. Moreover, we show that it is not possible to approximate the injective chromatic number of an undirected path graph within a factor of n1/3−ε in polynomial time for every ε>0 unless ZPP = NP. On the positive side, we prove that the injective chromatic number of an interval graph is either Δ(G) or Δ(G)+1, where Δ(G) is the maximum degree of G. We also characterize the interval graphs having χi(G)=Δ(G) and χi(G)=Δ(G)+1. As a consequence of this characterization, we obtain a linear time algorithm to find the injective chromatic number of an interval graph.

Sorting genomes by prefix double-cut-and-joins

In this paper, we study the problem of sorting unichromosomal linear genomes by prefix double-cut-and-joins (or DCJs) in both the signed and the unsigned settings. Prefix DCJs cut the leftmost segment of a genome and any other segment, and recombine the severed endpoints in one of two possible ways: one of these options corresponds to a prefix reversal, which reverses the order of elements between the two cuts (as well as their signs in the signed case). Our main results are: (1) new structural lower bounds based on the breakpoint graph for sorting by unsigned prefix reversals, unsigned prefix DCJs, and signed prefix DCJs; (2) two polynomial-time algorithms for sorting by prefix DCJs, both in the signed case (which answers an open question of Labarre [1]) and in the unsigned case; (3) a 1-absolute approximation algorithm for sorting by unsigned prefix reversals for a specific class of permutations.

Universal proof theory: Feasible admissibility in intuitionistic modal logics

We introduce a general and syntactically defined family of sequent-style calculi over the propositional language with the modalities {□,◇} and its fragments as a formalization for constructively acceptable systems. Calling these calculi constructive, we show that any strong enough constructive sequent calculus, satisfying a mild technical condition, feasibly admits all Visser's rules. This means that there exists a polynomial-time algorithm that, given a proof of the premise of a Visser's rule, provides a proof for its conclusion. As a positive application, we establish the feasible admissibility of Visser's rules in sequent calculi for several intuitionistic modal logics, including CK, IK, their extensions by the modal axioms T, B, 4, 5, and the axioms for bounded width and depth and their fragments CK□, propositional lax logic and IPC. On the negative side, we show that if a strong enough intuitionistic modal logic (satisfying a mild technical condition) does not admit at least one of Visser's rules, it cannot have a constructive sequent calculus. Consequently, no intermediate logic other than IPC has a constructive sequent calculus.

Value-Positivity for Matrix Games

Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that refine the notion of optimality in the context of polynomially perturbed matrix games. The first concept captures how the value depends on the perturbation parameter, and the second consists of the existence of a fixed strategy that guarantees the value of the unperturbed matrix game for every sufficiently small positive parameter. We provide polynomial-time algorithms to check whether a polynomially perturbed matrix game satisfies these properties. We further provide the functional form for a parameterized optimal strategy and the value function. Finally, we translate our results to linear programming and stochastic games, where value positivity is related to the existence of robust solutions. Funding: This research was supported by Fondation CFM pour la Recherche, the H2020 European Research Council [Grant ERC-CoG-863818 (ForM-SMArt)], the Austrian Science Fund [Grant 10.55776/COE12], ANID Chile [Grant ACT210005], and Agence Nationale de la Recherche [Grant ANR-21-CE40-0020].

Due date-oriented picker routing, an efficient exact solution algorithm, and its application to pick-from-store omnichannel retailing

The advent of e-commerce and omnichannel retailing has sparked renewed interest in picker routing in warehouses. This paper presents two significant methodological advances in this well-established field. First, it is a well-known fact that the parallel-aisle layout of warehouses, as opposed to general graphs, allows for polynomial-time solutions of the Traveling Salesman Problem. We show that the parallel-aisle structure can also be exploited when pickers are tasked with visiting storage positions associated with specific due dates. We establish that picker routing in warehouses, subject to soft due date constraints, is a binary NP-hard problem. We also present an exact branch-and-bound algorithm with pseudo-polynomial time complexity. This algorithm effectively solves instances with up to 60 picking positions and five cross aisles within a few seconds while guaranteeing optimality. Second, for even larger pick lists, we demonstrate the successful integration of our algorithm into a real-time framework. This approach allows us to avoid extended solution times that would otherwise delay the picker’s departure, without compromising the quality of the solution. To illustrate the practical relevance of these two methodological innovations, we apply our routing algorithm to the context of pick-from-store omnichannel retailing. By assigning due dates to critical products, we significantly reduce stockout occurrences for online customers. These stockouts occur when the stock level, initially deemed sufficient to confirm an online order, is depleted by walk-in customers before the picker reaches the relevant shelf.