Time Complexity Research Articles

Traffic Engineering with Specified Quality of Service Parameters in Software-defined Networks

A method of traffic engineering (TE) based on the method of multi-path routing is proposed in the study. Today, one of the main challenges in networking is to organize an efficient TE system that will provide such parameters of quality of service (QoS) as the allowable value of packet loss and time for traffic re-routing. Traditional one-way routing facilities do not provide the required quality of service (QoS) parameters for TE. Modern computer networks use static and dynamic routing algorithms, which are characterized by big time complexity and a large amount of service information. This negatively affects the overall state of the network, namely: leads to network congestion, device failure, loss of information during routing and increases the time for traffic re-routing. Research has shown that the most promising way to solve the TE problem in computer networks is a comprehensive approach, which consists of multi-path routing, SDN technology and monitoring of the overall situation of the network. This paper proposes a method of traffic engineering in a software-defined network with specified quality of service parameters, which has reduced the time of traffic re-routing and the percentage of packet loss due to the combination of the centralized TE method and multi-path routing. From a practical point of view, the obtained method, will improve the quality of service in computer networks in comparison with the known method of traffic construction.

Quantum Probabilistic Model Checking for Time-Bounded Properties

Probabilistic model checking (PMC) is a verification technique for analyzing the properties of probabilistic systems. However, existing techniques face challenges in verifying large systems with high accuracy. PMC struggles with state explosion, where the number of states grows exponentially with the size of the system, making large system verification infeasible. While statistical model checking (SMC) avoids PMC’s state explosion problem by using a simulation approach, it suffers from runtime explosion, requiring numerous samples for high accuracy. To address these limitations in verifying large systems with high accuracy, we present quantum probabilistic model checking (QPMC), the first method leveraging quantum computing for PMC with respect to time-bounded properties. QPMC addresses state explosion by encoding PMC problems into quantum circuits that superpose states within qubits. Additionally, QPMC resolves runtime explosion through Quantum Amplitude Estimation, efficiently estimating the probabilities of specified properties. We prove that QPMC correctly solves PMC problems and achieves a quadratic speedup in time complexity compared to SMC.

A Linear-Time Optimal Broadcasting Algorithm in Stars of Cliques

For the telephone broadcast model, an $O(n\log n)$-time algorithm for constructing an optimal broadcasting scheme in a star of cliques with a total of $n$ vertices was recently presented by Ambashankar and Harutyunyan at IWOCA 2024. In the present note we give a considerably shorter and purified algorithm description and correctness proof. Moreover, we improve the time complexity to $O(n)$.

Compiler Support for Sparse Tensor Convolutions

This paper extends prior work on sparse tensor algebra compilers to generate asymptotically efficient code for tensor expressions with affine subscript expressions. Our technique enables compiler support for a wide range of sparse computations, including sparse convolutions and pooling that are widely used in ML and graphics applications. We propose an approach that gradually rewrites compound subscript expressions to simple subscript expressions with loops that exploit the sparsity pattern of the input sparse tensors. As a result, the time complexity of the generated kernels is bounded by the number of stored elements and not by the shape of the tensors. Our approach seamlessly integrates into existing frameworks and is compatible with recent advances in compilers for sparse computations, including the flexibility to efficiently handle arbitrary combinations of different sparse tensor formats. The implementation of our algorithm is open source and upstreamed to the MLIR sparse compiler. Experimental results show that our method achieves 19.5x speedup when compared with the state-of-the-art compiler-based method at 99.9% sparsity. The generated sparse kernels start to outperform dense convolution implementations at about 80% sparsity.

Improving Differential-Neural Cryptanalysis

Our first objective is to enhance the capabilities of differential-neural distinguishers by applying more deep-learning techniques, focusing on handling more rounds and improving accuracy. Inspired by the Inception Block in GoogLeNet, we adopted a design that uses multiple parallel convolutional layers with varying kernel sizes before the residual block to capture multi-dimensional information. Additionally, we expanded the convolutional kernels in the residual blocks, enlarging the network's receptive field. In the case of Speck32/64, our efforts yield accuracy improvements in rounds 6, 7, and 8, enabling the successful training of a 9-round differential-neural distinguisher. As for Simon32/64, we developed a differential-neural distinguisher capable of effectively handling 12 rounds while achieving noteworthy accuracy enhancements in rounds 9, 10, and 11. Additionally, we utilized neutral bits to ensure the required data distribution for launching a successful key recovery attack when using multiple-ciphertext pairs as input for the neural network. Meanwhile, we redefined the formula for time complexity based on the differences in prediction speeds of the distinguisher between a single-core CPU and a GPU. Combining these various advancements allows us to considerably reduce the time and data complexity of key recovery attacks on 13-round Speck32/64. Furthermore, we used knowledge distillation techniques to reduce the model size, accelerating the distinguisher's prediction speed and reducing the time complexity. In particular, we achieved a successful 14-round key recovery attack by exhaustively guessing a 1-round subkey. For Simon32/64, we accomplished a 17-round key recovery attack for the first time and reduced the time complexity of the 16-round key recovery attack.

Computing Orientations from the Endomorphism Ring of Supersingular Curves and Applications

This work introduces several algorithms related to the computation of orientations in endomorphism rings of supersingular elliptic curves. This problem is at the heart of several results regarding the security of oriented-curves in isogeny-based cryptography. Under the Deuring correspondence, it can be expressed purely in terms of quaternion and boils down to representing integers by ternary quadratic forms. Our main contribution is to show that there exist efficient algorithms to solve this problem for quadratic orders of discriminant n up to O ( p 4 / 3 ) . Our approach improves upon previous results by increasing this bound from O ( p ) to O ( p 4 / 3 ) and removing some heuristics. We introduce several variants of our new algorithm and provide a careful analysis of their asymptotic running time (without heuristic when it is possible). The best proven asymptotic complexity of one of our variants is O ( n 3 / 4 / p ) in average. The best heuristic variant has a complexity of O ( p 1 / 3 ) for big enough n . We then introduce several results regarding the computation of ideals between oriented orders. The first application of this is a simplification of the known reduction from vectorization to computing the endomorphism ring, removing the assumption on the factorization of the discriminant. As a second application, we relate the problem of computing fixed-degree isogenies between supersingular curves to the problem of computing orientations in endomorphism rings, and we show that for a large range of degree d , our new algorithms improve on the state-of-the-art, and in important special cases, the range of degree d for which there exist a polynomial-time algorithm is increased. In the most special case we consider, when both curves are oriented by a small degree endomorphism, we show heuristically that our techniques allow the computation of isogenies of any degree, assuming they exist.

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.