Time Complexity Research Articles

An efficient PGD solver for structural dynamics applications

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the implementation of a solver that is halfway between Modal Decomposition and the conventional PGD framework, so as to accelerate the fixed-point iteration algorithm. Additional procedures such that Aitken’s delta-squared process and mode-orthogonalization are incorporated to ensure convergence and stability of the algorithm. Numerical results regarding the ROM accuracy, time complexity, and scalability are provided to demonstrate the performance of the new solver when applied to dynamic simulation of a three-dimensional structure.

The nearest graph Laplacian in Frobenius norm

AbstractWe address the problem of finding the nearest graph Laplacian to a given matrix, with the distance measured using the Frobenius norm. Specifically, for the directed graph Laplacian, we propose two novel algorithms by reformulating the problem as convex quadratic optimization problems with a special structure: one based on the active set method and the other on direct computation of Karush–Kuhn–Tucker points. The proposed algorithms can be applied to system identification and model reduction problems involving Laplacian dynamics. We demonstrate that these algorithms possess lower time complexities and the finite termination property, unlike the interior point method and V‐FISTA, the latter of which is an accelerated projected gradient method. Our numerical experiments confirm the effectiveness of the proposed algorithms.

A fast H.266/QTMT intra coding scheme based on predictions of learned models

ABSTRACT H.266/VVC adopts a QuadTree-plus-MultiType tree (QTMT) coding-unit (CU) split structure to improve efficiency at the cost of high time complexity. Speeding up VVC coding while minimizing quality degradation is critical for practical applications. We propose predicting the coding depth and split type of an optimally coded 32 × 32 CU (CU32 × 32) to perform only a subset of exhaustive rate-distortion optimization (RDO) operations: (1) To predict the depth of an optimally coded CU32 × 32, we train a convolutional neural network (CNNdepth). CNNdepth outputs a label specifying a depth range subset by which the controller can execute EarlySkip or EarlyTerminate to reduce time complexity. (2) To predict the split type, we train random forest classifiers (RFCtype). The corresponding RDO operations can be omitted if the RFCtype classifies one CU32 × 32 as not of a specified split type. Experiments show that CNNdepth and RFCtype work seamlessly, reducing execution time by up to 69% and 39.16% on average, with a 0.7% increase in BDBR compared to the default VTM-7.0. Additionally, the proposed method yields the highest balanced time reduction rate of 61.5%.

Governing Complexity in Complex Times: The HDP Nexus and the Role of the UN, the EU and the World Bank

ABSTRACT Based on the work conducted with a Nexus-centred network of scholars and practitioners (HDP LAB SYNEX4 Future), an overview is offered of the literature on regime complexity to analyse origins and evolution of the Triple Nexus multilateral approach to the governance of compound humanitarian-development-security crises. Identifying the main institutional features of the UN-orchestrated Nexus policy concept highlights its potential as an innovative attempt at global experimentalist governance. This analysis of the nexus-based approach of the United Nations (UN), the European Union (EU) and the World Bank Group (WBG) in three pilot countries – Cameroon, Myanmar and the Democratic Republic of Congo (DRC) – demonstrates that, while coordination has increased, the agency of local communities remains limited and major impediments hinder the inclusion of the peace dimension, an area where separate initiatives by non-Western regional organisations have also stalled. Progress will necessarily depend on the ability of Nexus actors to develop its bottom-up and participatory components, and to improve coordination within the group of like-minded donors who share a clear commitment to a human rights-based, inclusive and prosperous future.

Randomized Trial of the Effectiveness of Videoconferencing-Based Versus Message-Based Psychotherapy on Depression.

The authors compared the engagement, clinical outcomes, and adverse events of text or voice message-based psychotherapy (MBP) versus videoconferencing-based psychotherapy (VCP) among adults with depression. The study used a sequential multiple-assignment randomized trial design with data drawn from phase 1 of a two-phase small business innovation research study. In total, 215 adults (ages ≥18 years) with depression received care from Talkspace, a digital mental health care company. Participants were initially randomly assigned to receive either asynchronous MBP or weekly VCP. All therapists provided evidence-based treatments such as cognitive-behavioral therapy. After 6 weeks of treatment, participants whose condition did not show a response on the Patient Health Questionnaire-9 or was rated as having not improved on the Clinical Global Impressions scale were randomly reassigned to receive either weekly VCP plus MBP or monthly VCP plus MBP. Longitudinal mixed-effects models with piecewise linear time trends applied to multiple imputed data sets were used to address missingness of data. Participants who were initially assigned to the MBP condition engaged with their therapists over more weeks than did participants in the VCP condition (7.8 weeks for MBP vs. 4.9 weeks for VCP; p<0.001). No meaningful differences were observed between the two groups in rates of change by 6 or 12 weeks for depression, anxiety, disability, or global ratings of improvement. Neither treatment resulted in any adverse events. MBP appears to be a viable alternative to VCP for treating adults with depression.

GSearch: ultra-fast and scalable genome search by combining K-mer hashing with hierarchical navigable small world graphs.

Genome search and/or classification typically involves finding the best-match database (reference) genomes and has become increasingly challenging due to the growing number of available database genomes and the fact that traditional methods do not scale well with large databases. By combining k-mer hashing-based probabilistic data structures (i.e. ProbMinHash, SuperMinHash, Densified MinHash and SetSketch) to estimate genomic distance, with a graph based nearest neighbor search algorithm (Hierarchical Navigable Small World Graphs, or HNSW), we created a new data structure and developed an associated computer program, GSearch, that is orders of magnitude faster than alternative tools while maintaining high accuracy and low memory usage. For example, GSearch can search 8000 query genomes against all available microbial or viral genomes for their best matches (n= ∼318 000 or ∼3 000 000, respectively) within a few minutes on a personal laptop, using ∼6 GB of memory (2.5 GB via SetSketch). Notably, GSearch has an O(log(N)) time complexity and will scale well with billions of genomes based on a database splitting strategy. Further, GSearch implements a three-step search strategy depending on the degree of novelty of the query genomes to maximize specificity and sensitivity. Therefore, GSearch solves a major bottleneck of microbiome studies that require genome search and/or classification.

Neural patient-specific 3D-2D registration in laparoscopic liver resection.

Augmented reality guidance in laparoscopic liver resection requires the registration of a preoperative 3D model to the intraoperative 2D image. However, 3D-2D liver registration poses challenges owing to the liver's flexibility, particularly in the limited visibility conditions of laparoscopy. Although promising, the current registration methods are computationally expensive and often necessitate manual initialisation. The first neural model predicting the registration (NM) is proposed, represented as 3D model deformation coefficients, from image landmarks. The strategy consists in training a patient-specific model based on synthetic data generated automatically from the patient's preoperative model. A liver shape modelling technique, which further reduces time complexity, is also proposed. The NM method was evaluated using the target registration error measure, showing an accuracy on par with existing methods, all based on numerical optimisation. Notably, NM runs much faster, offering the possibility of achieving real-time inference, a significant step ahead in this field. The proposed method represents the first neural method for 3D-2D liver registration. Preliminary experimental findings show comparable performance to existing methods, with superior computational efficiency. These results suggest a potential to deeply impact liver registration techniques.

Technique for Kernel Matching Pursuit Based on Intuitionistic Fuzzy c-Means Clustering

Kernel matching pursuit (KMP) requires every step of the searching process to be global optimal searching in the redundant dictionary of functions in order to select the best matching signal structure. Namely, the dictionary learning time of KMP is too long. To solve the above drawbacks, a rough dataset was divided into some small-sized dictionaries to substitute local searching for global searching by using the property superiority of dynamic clustering performance, which is also superior in the intuitionistic fuzzy c-means (IFCM) algorithm. Then, we proposed a novel technique for KMP based on IFCM (IFCM-KMP). Subsequently, three tests including classification, effectiveness, and time complexity were carried out on four practical sample datasets, the conclusions of which fully demonstrate that the IFCM-KMP algorithm is superior to FCM and KMP.

Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity

This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R2, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of n points distributed bleast-bmost-boundedly in some rectangle can be determined with the complexity O(n). Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.

On-Chain Verifiable Credential with Applications in Education

A verifiable credential (VC) has been standardized and applied in various domains, including education. Due to its immutability, blockchain has been considered and used for credential issuance and verification. Most existing methods, however, are not compatible with the W3C VC standard. In this paper, an on-chain VC issuance and verification method has been described. The method is based on the standard VC data model and applicable to any credential type. It decomposes a VC document into a VC template and the corresponding value array(s). This allows a VC to be issued on-chain in the Bitcoin BTC network, which has a limited data embedding capacity. The proposed method reduces blockchain resource consumption due to the reusability of a VC template. In addition, it allows the use of a concise VC fingerprint format instead of a full VC for credential exchange. Two issuance modes, namely the full on-chain and partial on-chain, are proposed targeting different use cases. The proposed method has been applied for issuing and verifying two learning credential types. The method was evaluated on the Bitcoin Testnet to measure time and space complexities. With the reduced-size VC fingerprint, the proposed method can embed a VC on a traditional paper-based credential as a compact-sized QR code. The proposed method offered faster VC issuance and verification than an existing standard-based verifiable credential method.

The Longest Wave Subsequence Problem: Generalizations of the Longest Increasing Subsequence Problem

The longest increasing subsequence (LIS) problem aims to find the subsequence exhibiting an increasing trend in a numeric sequence with the maximum length. In this paper, we generalize the LIS problem to the longest wave subsequence (LWS) problem, which encompasses two versions: LWSt and LWSr. Given a numeric sequence [Formula: see text] of distinct values and a target trend sequence [Formula: see text], the LWSt problem aims to identify the longest subsequence of [Formula: see text] that preserves the trend of the prefix of [Formula: see text]. And, the LWSr problem aims to find the longest subsequence of [Formula: see text] within [Formula: see text] segments, alternating increasing and decreasing subsequences. We propose two efficient algorithms for solving the two versions of the LWS problem. For the LWSt problem, the time complexity of our algorithm is O[Formula: see text], where [Formula: see text] represents the length of the given numeric sequence [Formula: see text]. Additionally, we propose an O[Formula: see text]-time algorithm for solving the LWSr problem. In both algorithms, we utilize the priority queues for the insertion, deletion, and successor operations.

Lower Bounds on the Amortized Time Complexity of Shared Objects

Lower Bounds on the Amortized Time Complexity of Shared Objects

Compact and Low-Latency FPGA-Based Number Theoretic Transform Architecture for CRYSTALS Kyber Postquantum Cryptography Scheme

In the modern era of the Internet of Things (IoT), especially with the rapid development of quantum computers, the implementation of postquantum cryptography algorithms in numerous terminals allows them to defend against potential future quantum attack threats. Lattice-based cryptography can withstand quantum computing attacks, making it a viable substitute for the currently prevalent classical public-key cryptography technique. However, the algorithm’s significant time complexity places a substantial computational burden on the already resource-limited chip in the IoT terminal. In lattice-based cryptography algorithms, the polynomial multiplication on the finite field is well known as the most time-consuming process. Therefore, investigations into efficient methods for calculating polynomial multiplication are essential for adopting these quantum-resistant lattice-based algorithms on a low-profile IoT terminal. Number theoretic transform (NTT), a variant of fast Fourier transform (FFT), is a technique widely employed to accelerate polynomial multiplication on the finite field to achieve a subquadratic time complexity. This study presents an efficient FPGA-based implementation of number theoretic transform for the CRYSTAL Kyber, a lattice-based public-key cryptography algorithm. Our hybrid design, which supports both forward and inverse NTT, is able run at high frequencies up to 417 MHz on a low-profile Artix7-XC7A100T and achieve a low latency of 1.10μs while achieving state-of-the-art hardware efficiency, consuming only 541-LUTs, 680 FFs, and four 18 Kb BRAMs. This is made possible thanks to the newly proposed multilevel pipeline butterfly unit architecture in combination with employing an effective coefficient accessing pattern.

On suffix tree detection

A suffix tree is a fundamental data structure for string processing and information retrieval, however, its structure is still not well understood. The suffix trees reverse engineering problem, which its research aims at reducing this gap, is the following. Given an ordered rooted tree T with unlabeled edges, determine whether there exists a string w such that the unlabeled-edges suffix tree of w is isomorphic to T. Previous studies on this problem consider the relaxation of having the suffix links as well as assume a binary alphabet. This paper is the first to consider the suffix tree detection problem, in which the relaxation of having suffix links as input is removed. We study suffix tree detection on two scenarios that are interesting per se. We provide a suffix tree detection algorithm for general alphabet periodic strings. Given an ordered tree T with n leaves, our detection algorithm takes O(n+|Σ|p)-time, where p is the unknown in advance length of a period that repeats at least 3 times in a string S having a suffix tree structure identical to T, if such S exists. Therefore, it is a polynomial time algorithm if p is a constant and a linear time algorithm if, in addition, the alphabet has a sub-linear size. We also show some necessary (but insufficient) conditions for binary alphabet general strings suffix tree detection. By this we take another step towards understanding suffix trees structure.

RNE-DSNet: A Re-parameterization Neighborhood Enhancement-based Dual-Stream Network for CT image recognition

Deep learning models based on Transformer and CNN are current research hotspots. However, there are more time complexity and space complexity in extracting global–local features, the feature extraction ability is insufficient for small lesions in CT images. A Re-parameterization Neighborhood Enhancement-based Dual-Stream Network (RNE-DSNet) is proposed for CT image recognition in this paper. This method improves the ability to recognize small lesions while reducing the Params number and FLOPs, which gives a trade-off between performance and cost. The main works are as following: Firstly, a Re-parameterization Neighborhood Enhancement-based Dual-Stream Network is designed to improve the global–local feature extraction ability. Secondly, the Re-parameterization Group Residual Block is designed in the CNN branch, which improves the local feature extraction ability through multi-scale and multi-branch structures, and the number of the Params and FLOPs are reduced effectively. The Neighborhood Enhancement Transformer Block is designed in the Transformer branch, in which the global attention is calculated by parallel Hadamard product and Dot product, and the global attention maps are enhanced by deep convolution operation to embed local features in global features. Thirdly, the Adaptive-random Mask Cropping method is designed to improve the features extraction ability for small lesions in CT images through heat map and random Mask techniques. RNE-DSNet is compared with other SOTA models. The Accuracy (ACC), Precision (PRE), Recall (REC), F1 score (F1), and Area Under Curve (AUC) values of RNE-DSNet are reached 99.22%, 99.23%, 99.08%, 99.23% and 99.38%, respectively, which verified the effectiveness of the RNE-DSNet model. The number Params and FLOPs are reduced by 62.78% and 84.20%, respectively. The effectiveness of RNE-DSNet is verified by heat map visualization. The performance of RNE-DSNet is generally better than the others methods. There is positive significance for computer aided diagnosis.

Decoding of MDP Convolutional Codes over the Erasure Channel under Linear Systems Point of View

This paper attempts to highlight the decoding capabilities of MDP convolutional codes over the erasure channel by defining them as discrete linear dynamical systems, with which the controllability property and the observability characteristics of linear system theory can be applied, in particular those of output observability, easily described using matrix language. Those are viewed against the decoding capabilities of MDS block codes over the same channel. Not only is the time complexity better but the decoding capabilities are also increased with this approach because convolutional codes are more flexible in handling variable-length data streams than block codes, where they are fixed-length and less adaptable to varying data lengths without padding or other adjustments.

Limitations to extracellular concentration sensing through signaling cascades

Signaling cascades refer to sequential biochemical reactions that occur in the cytoplasm of living cells in response to the binding of a ligand to a cell surface receptor, triggering a cellular response. Living cells need to sense extracellular concentrations with high precision. In this paper, we study the limitations of extracellular concentration measurement in linear signaling cascades. We find that as long as the cascade is linear and measurement times are much larger or much smaller than the timescales of the cytoplasmic reactions, the error in concentration measurement is independent of cascade length, the nature of the reactions and their rates. Our results can also be extended to generic non-linear signal cascades when the measurement time is much smaller than the timescales of cytoplasmic reactions. We illustrate this by considering the specific example of the accuracy of concentration detection in E. coli.

Sparse transformer with local and seasonal adaptation for multivariate time series forecasting

Transformers have achieved remarkable performance in multivariate time series(MTS) forecasting due to their capability to capture long-term dependencies. However, the canonical attention mechanism has two key limitations: (1) its quadratic time complexity limits the sequence length, and (2) it generates future values from the entire historical sequence. To address this, we propose a Dozer Attention mechanism consisting of three sparse components: (1) Local, each query exclusively attends to keys within a localized window of neighboring time steps. (2) Stride, enables each query to attend to keys at predefined intervals. (3) Vary, allows queries to selectively attend to keys from a subset of the historical sequence. Notably, the size of this subset dynamically expands as forecasting horizons extend. Those three components are designed to capture essential attributes of MTS data, including locality, seasonality, and global temporal dependencies. Additionally, we present the Dozerformer Framework, incorporating the Dozer Attention mechanism for the MTS forecasting task. We evaluated the proposed Dozerformer framework with recent state-of-the-art methods on nine benchmark datasets and confirmed its superior performance. The experimental results indicate that excluding a subset of historical time steps from the time series forecasting process does not compromise accuracy while significantly improving efficiency. Code is available at https://github.com/GRYGY1215/Dozerformer.

On Upward-Planar L-Drawings of Graphs

In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge $e=(v,w)$ is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail $v$ of $e$ and of a horizontal segment ending at the head $w$ of $e$. Distinct edges may overlap, but must not cross. Recently, upward-planar L-drawings have been studied for $st$-graphs, i.e., planar DAGs with a single source $s$ and a single sink $t$ containing an edge directed from $s$ to $t$. It is known that a plane $st$-graph, i.e., an embedded $st$-graph in which the edge $(s,t)$ is incident to the outer face, admits an upward-planar L-drawing if and only if it admits a bitonic $st$-ordering, which can be tested in linear time. % We study upward-planar L-drawings of DAGs that are not necessarily $st$-graphs. As a combinatorial result, we show that a plane DAG admits an upward-planar L-drawing if and only if it is a subgraph of a plane $st$-graph admitting a bitonic $st$-ordering. This allows us to show that not every tree with a fixed bimodal embedding admits an upward-planar L-drawing. Moreover, we prove that any directed acyclic cactus with a single source (or a single sink) admits an upward-planar L-drawing, which respects a given outerplanar~embedding if there are no transitive edges. On the algorithmic side, we consider DAGs with a single source (or a single sink). We give linear-time testing algorithms for these DAGs in two cases: (a) when the drawing must respect a prescribed embedding and (b) when no restriction is given on the embedding, but the underlying undirected graph is series-parallel. For the single-sink case of (b) it even suffices that each biconnected component is series-parallel.

Modeling Sequences as Star Graphs to Address Over-smoothing in Self-attentive Sequential Recommendation

Self-attention (SA) mechanisms have been widely used in developing sequential recommendation (SR) methods, and demonstrated state-of-the-art performance. However, in this paper, we show that self-attentive SR methods substantially suffer from the over-smoothing issue that item embeddings within a sequence become increasingly similar across attention blocks. As widely demonstrated in the literature, this issue could lead to a loss of information in individual items, and significantly degrade models’ scalability and performance. To address the over-smoothing issue, in this paper, we view items within a sequence constituting a star graph and develop a method, denoted as MSSG, for SR. Different from existing self-attentive methods, MSSG introduces an additional internal node to specifically capture the global information within the sequence, and does not require information propagation among items. This design fundamentally addresses the over-smoothing issue and enables MSSG a linear time complexity with respect to the sequence length. We compare MSSG with eleven state-of-the-art baseline methods on six public benchmark datasets. Our experimental results demonstrate that MSSG significantly outperforms the baseline methods, with an improvement of as much as 10.10%. Our analysis shows the superior scalability of MSSG over the state-of-the-art self-attentive methods. Our complexity analysis and run-time performance comparison together show that MSSG is both theoretically and practically more efficient than self-attentive methods. Our analysis of the attention weights learned in SA-based methods indicates that on sparse recommendation data, modeling dependencies in all item pairs using the SA mechanism yields limited information gain, and thus, might not benefit the recommendation performance. Our source code and data are publicly accessible through GitHub .