Running Time Of Algorithm Research Articles

PAM: Predictive analytics and modules‐based computation offloading framework using greedy heuristics and 5G NR‐V2X

AbstractRecent advancements in distributed computing systems have shown promising prospects in enabling the effective usage of many next‐generation applications. These applications include a wide range of fields, such as healthcare, interactive gaming, video streaming, and other related technologies. Among such solutions are the evolving vehicular fog computing (VFC) frameworks that make use of IEEE and 3GPP protocols and use advanced optimization algorithms. However, these approaches often rely on outdated protocols or computationally intensive mathematical techniques for solving or representing their optimization models. Additionally, some of these frameworks have not thoroughly considered the type of application during their evaluation and validation phases. In response to these challenges, we have developed the “predictive analytics and modules” (PAM) framework, which operates on a time and event‐driven basis. It utilizes up‐to‐date 3GPP protocols to address the inherent unpredictability of VFC‐enabled distributed computing systems required in smart healthcare systems. Through a combination of a greedy heuristic approach and a distributed offloading architecture, PAM efficiently optimizes decisions related to task offloading and computation allocation. This is achieved through specialized algorithms that provide support to computationally weaker devices, all within a time frame of under 100 ms. To assess the performance of PAM in comparison to three benchmark methodologies, the evaluation pathways that we employed are average response time, probability density function, pareto‐analysis, algorithmic run time, and algorithmic complexity.

Graph-Based vs. Error State Kalman Filter-Based Fusion of 5G and Inertial Data for MAV Indoor Pose Estimation

5G New Radio Time of Arrival (ToA) data has the potential to revolutionize indoor localization for micro aerial vehicles (MAVs). However, its performance under varying network setups, especially when combined with IMU data for real-time localization, has not been fully explored so far. In this study, we develop an Error State Kalman Filter (ESKF) and a Pose Graph Optimization (PGO) approach to address this gap. We systematically evaluate the performance of the derived approaches for real-time MAV localization in realistic scenarios with 5G base stations in Line-Of-Sight (LOS), demonstrating the potential of 5G technologies in this domain. In order to experimentally test and compare our localization approaches, we augment the EuRoC MAV benchmark dataset for visual-inertial odometry with simulated yet highly realistic 5G ToA measurements. Our experimental results comprehensively assess the impact of varying network setups, including varying base station numbers and network configurations, on ToA-based MAV localization performance. The findings show promising results for seamless and robust localization using 5G ToA measurements, achieving an accuracy of 15 cm throughout the entire trajectory within a graph-based framework with five 5G base stations, and an accuracy of up to 34 cm in the case of ESKF-based localization. Additionally, we measure the run time of both algorithms and show that they are both fast enough for real-time implementation.

A novel hybrid algorithm for two-dimensional direction-of-arrival estimation in massive MIMO systems

Massive Multiple-Input Multiple-Output (mMIMO) systems have been significantly exploited to enhance mobile network capacity. Increasing the number of antennas provided higher direction-of-arrival (DOA) estimation accuracy, especially when utilizing a two-dimensional multi-signal classification algorithm (2D-MUSIC). However, this algorithm suffers from the heavy computational complexity imposed by the 2D angle search. This paper proposes a novel hybrid algorithm called the 2D-MM, which combines the strengths of the 2D-MUSIC algorithm with the 2D-Minimum Variance Distortionless Response (2D-MVDR) algorithm to reduce the computational complexity using a fast new DOAs search strategy. To be more precise, the new search strategy involves two stages: the 2D-MVDR stage detects the approximate DOAs within a whole angular field of view using as few antennas as possible and snapshots of received data. Then, the 2D-MUSIC stage accurately determines the number and locations (azimuths and elevations) of those sources within the angular sectors in which they appear. Furthermore, the choice of utilizing a uniform circular array (UCA) configuration for representing mMIMO systems is enhanced by introducing a new geometric structure featuring two concentric rings. The simulation results indicate that confining the spectral peak searching process into octant areas with an angular sector spanning π⁄4 instead of the total angular field of view (0–2π) would avoid searching empty areas and then reduce the computational complexity, where the improvement percentage in the proposed algorithm's running time was approaching 80 % when utilized with mMIMO arrays. In contrast, the proposed algorithm proves effective for mMIMO systems, irrespective of the increased number of antennas utilized.

3D Refraction Travel Time Accuracy Study in High Contrasted Media

Among all the existing methods to solve the eikonal equation, three methods are chosen to verify accuracy, symmetry, reciprocity and error propagation along large offsets of refracted waves in seismic near surface exploration context. Performance is extremely highlighted nowadays and accuracy is being neglected, then an eikonal solver poorly explored in geoscience is used. A classical solver, the Fast Iterative and the modified Fast Sweeping Method are applied in three modeling schemes: a simple two layers model, a large four layers and a complex benchmark model. The three methods compute the first arrival of refracted waves in high contrast media and the results are compared to the analytical solution. A circular geometry is considered in all experiments to explore the method applicability using full azimuth angles. On the first scheme, the errors in travel time are computed among the three methods using different model sample spacing and we discuss accuracy, symmetry and reciprocity of first arrivals. On the second scheme, three circular receivers are placed in different offsets to check errors along refracted wave propagation. Finally, the third scheme, four shots are strategically positioned over the SEG/EAGE Overthrust model in order to compare the full acoustic wavefield with the eikonal solvers and then check the similarities. Although the focus is on methods accuracy, the algorithm run time is also considered and the comparison shows that the modified Fast Sweeping Method is the most accurate. The most computational efficient eikonal solver is the Fast Iterative Method, but its geoscience applicability needs to be cautious, because of its inaccurate results.

Models for Test Cost Minimization in Database Migration

Database migration is a ubiquitous need faced by enterprises that generate and use vast amounts of data. This is because of database software updates, or it is from changes to hardware, project standards, and other business factors. Migrating a large collection of databases is a way more challenging task than migrating a single database because of the presence of additional constraints. These constraints include capacities of shifts and sizes of databases. In this paper, we present a comprehensive framework that can be used to model database migration problems of different enterprises with customized constraints by appropriately instantiating the parameters of the framework. These parameters are the size of each database, the size of each shift, and the cost of testing each application. Each of these parameters can be either constant or arbitrary. Additionally, the cost of testing an application can be proportional to the number of databases that the application uses. We establish the computational complexities of a number of instantiations of this framework. We present fixed-parameter intractability results for various relevant parameters of the database migration problem. We also provide approximability and inapproximability results as well as lower bounds for the running time of any exact algorithm for the database migration problem. We show that the database migration problem is equivalent to a variation of the classical hypergraph partitioning problem. Our theoretical results also imply new theoretical results for the hypergraph partitioning problem that are interesting in their own right. Finally, we adapt heuristic algorithms devised for the hypergraph partitioning problem to the database migration problem, and we also give experimental results for the adapted heuristics. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: B. Caskurlu and U. U. Acikalin are supported by The Scientific and Technological Research Council of Türkiye [Grant 122E599]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0021 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0021 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Constructing and sampling partite, 3-uniform hypergraphs with given degree sequence.

Partite, 3-uniform hypergraphs are 3-uniform hypergraphs in which each hyperedge contains exactly one point from each of the 3 disjoint vertex classes. We consider the degree sequence problem of partite, 3-uniform hypergraphs, that is, to decide if such a hypergraph with prescribed degree sequences exists. We prove that this decision problem is NP-complete in general, and give a polynomial running time algorithm for third almost-regular degree sequences, that is, when each degree in one of the vertex classes is k or k - 1 for some fixed k, and there is no restriction for the other two vertex classes. We also consider the sampling problem, that is, to uniformly sample partite, 3-uniform hypergraphs with prescribed degree sequences. We propose a Parallel Tempering method, where the hypothetical energy of the hypergraphs measures the deviation from the prescribed degree sequence. The method has been implemented and tested on synthetic and real data. It can also be applied for χ2 testing of contingency tables. We have shown that this hypergraph-based χ2 test is more sensitive than the standard χ2 test. The extra sensitivity is especially advantageous on small data sets, where the proposed Parallel Tempering method shows promising performance.

Improved genetic algorithm based on rule optimization strategy for fibre allocation

ABSTRACT In modern manufacturing industry, in order to adapt to changes in the general environment, the manufacturing industry must improve production efficiency. To this end, this article introduces an improved genetic algorithm based on rule selection to tackle the nondeterministic polynomial hard problem stemming from inventory fibre resources and fibre selection principles in optical cable production. The algorithm aims to maximize inventory score and minimize fibre segmentation rate. It employs a permutation encoding approach to link the genetic algorithm with fibre allocation solutions and applies a self-attention mechanism to determine subset solution weight within each solution. To boost the recombination of favourable gene segments from different chromosomes, a rule optimization strategy is integrated into the crossover operation based on the weights. This operations enhance the algorithm's global search capability and convergence speed. A feasibility repair strategy is then used to inspect and rectify chromosomes, preventing the generation of illegal solutions. The legitimate mutation operation, founded on weight optimization rules, effectively reduces the algorithm's running time by avoiding illegal solutions. By leveraging actual production data from an optical cable manufacturer for simulation, the experimental results confirm the effectiveness of the improved genetic algorithm in addressing the fibre allocation problem. Comparative simulations with the unimproved genetic algorithm and a stepwise greedy algorithm underscore the superiority of the improved genetic algorithm in resolving the fibre allocation problem.

Accelerating regularized tensor decomposition using the alternating direction method of multipliers with multiple Nesterov’s extrapolations

Tensor decomposition is an essential tool for multiway signal processing. At present, large-scale high-order tensor data require fast and efficient decomposing algorithms. In this paper, we propose accelerated regularized tensor decomposition algorithms using the alternating direction method of multipliers with multiple Nesterov’s extrapolations in the block coordinate descent framework. We implement the acceleration in three cases: only in the inner loop, only in the outer loop, and in both the inner and outer loops. Adaptive safeguard strategies are developed following the acceleration to guarantee monotonic convergence. Afterwards, we utilize the proposed algorithms to accelerate two types of conventional decomposition: nonnegative CANDECOMP/PARAFAC (NCP) and sparse CANDECOMP/PARAFAC (SCP). The experimental results on synthetic and real-world tensors demonstrate that the proposed algorithms achieve significant acceleration effects and outperform state-of-the-art algorithms. The accelerated algorithm with extrapolations in both the inner and outer loops has the fastest convergence speed and takes almost one-third of the running time of typical algorithms.

BYO: A Unified Framework for Benchmarking Large-Scale Graph Containers

A fundamental building block in any graph algorithm is a graph container - - a data structure used to represent the graph. Ideally, a graph container enables efficient access to the underlying graph, has low space usage, and supports updating the graph efficiently. In this paper, we conduct an extensive empirical evaluation of graph containers designed to support running algorithms on large graphs. To our knowledge, this is the first apples-to-apples comparison of graph containers rather than overall systems, which include confounding factors such as differences in algorithm implementations and infrastructure. We measure the running time of 10 highly-optimized algorithms across over 20 different containers and 10 graphs. Somewhat surprisingly, we find that the average algorithm running time does not differ much across containers, especially those that support dynamic updates. Specifically, a simple container based on an off-the-shelf B-tree is only 1.22× slower on average than a highly optimized static one. Moreover, we observe that simplifying a graph-container Application Programming Interface (API) to only a few simple functions incurs a mere 1.16× slowdown compared to a complete API. Finally, we also measure batch-insert throughput in dynamic-graph containers for a full picture of their performance. To perform the benchmarks, we introduce BYO, a unified framework that standardizes evaluations of graph-algorithm performance across different graph containers. BYO extends the Graph Based Benchmark Suite (Dhulipala et al. 18), a state-of-the-art graph algorithm benchmark, to easily plug into different dynamic graph containers and enable fair comparisons between them on a large suite of graph algorithms. While several graph algorithm benchmarks have been developed to date, to the best of our knowledge, BYO is the first system designed to benchmark graph containers.

An Optimised Hoffman Algorithm for Testing Linear Code Equivalency

The Hoffman’s algorithm to test equivalency of linear codes is one of the techniques that have been used over the years; it is achieved by a comparison of codewords of the linear codes. However, this comparison technique becomes ineffective in instances where it is applied to linear codes with larger dimensions as it requires much run time complexity, space and size in comparing the codewords of each linear code. This paper proposes an optimised algorithm for testing the equivalency of linear codes, specifically addressing the limitations of the Hoffman method. To assess and compare the efficiencies of the Hoffman algorithm and the optimised algorithm, a set of nine carefully selected linear codes were subjected to equivalency testing. The CPU runtime of both algorithms was recorded using the C++ chrono library. The recorded runtime data was then utilized to create a scatter plot, offering a visual representation of the contrasting trends in CPU runtime between the two algorithms. The plot clearly indicate exponential growth in CPU runtime for the Hoffman algorithm as the length and dimension of the linear codes increases, in contrast, the proposed algorithm showcased a minimal growth in CPU runtime, indicating its superior efficiency and optimised performance.

A Cable-Based Haptic Interface with a Reconfigurable Structure

Abstract Cable robots have been used as haptic interfaces for several decades now, with the most notable examples being the SPIDAR and its numerous iterations throughout the years, as well as the more recent IPAnema 3 Mini manufactured by Fraunhofer IPA. However, these robots still have drawbacks, particularly their high number of cables required to maintain a high workspace-to-installation-space ratio. Using a hybrid-structure cable robot (HSCR) could prevent some collisions that occur between the cables and the user's body. More specifically, some applications requiring multimodal feedback could benefit from the flexibility that a reduced number of cables offers. Therefore, this paper presents a novel SPIDAR-like VSCR and its sensor-less force control method based on motor current. The purpose of this work is to clarify the advantages that a variable structure can provide for haptic interaction. In this regard, experimental results regarding the device's workspace and its force feedback capabilities are presented. Additionally, since real-time high-frequency updates are required for haptic display, we provide additional data regarding the control algorithm's runtime. Lastly, another experiment was conducted to study changes in user performance when using both the variable and the usual cable configuration. The results showed that feedback accuracy is maintained, and there are no drawbacks to using hybrid configurations.

Multiobjective route finding in a multimode transportation network by NSGA-II

Route finding is an everyday challenge for urban residents. While many route planner applications exist, they cannot find suitable routes based on user preferences. According to user preferences, routing in a multimode urban transportation network can be considered a multiobjective optimization problem. Different objectives and modes for transportation, along with many routes as decision elements, give rise to the complexity of the problem. This study uses an elitism multiobjective evolutionary algorithm and the Pareto front concept to solve the problem. The data of a simulated multimode network consisting of 150 vertexes and 2600 edges are used to test and evaluate the proposed method. Four transport modes are considered: the metro, bus, taxi, and walking. Also, three minimization objective functions are considered: expense, discomfort, and time. The results show the competence of the algorithm in solving such a complex problem in a short run time. The optimal setting for the algorithm parameters is found by considering the algorithm run time, diversity of solutions, and convergence trend by running sensitivity analyses. A repeatability test is applied using the optimal setting of the algorithm, which shows a high level of repeatability. While NSGA-II (Non-dominated Sorting Genetic Algorithm II) may be a well-established algorithm in the literature, its application in multiobjective route finding in multimode transport networks is unique and novel. The outcomes of the proposed method are compared with existing methods in the literature, proving the better performance of the NSGA-II algorithm.

Automatic and real-time tissue sensing for autonomous intestinal anastomosis using hybrid MLP-DC-CNN classifier-based optical coherence tomography.

Anastomosis is a common and critical part of reconstructive procedures within gastrointestinal, urologic, and gynecologic surgery. The use of autonomous surgical robots such as the smart tissue autonomous robot (STAR) system demonstrates an improved efficiency and consistency of the laparoscopic small bowel anastomosis over the current da Vinci surgical system. However, the STAR workflow requires auxiliary manual monitoring during the suturing procedure to avoid missed or wrong stitches. To eliminate this monitoring task from the operators, we integrated an optical coherence tomography (OCT) fiber sensor with the suture tool and developed an automatic tissue classification algorithm for detecting missed or wrong stitches in real time. The classification results were updated and sent to the control loop of STAR robot in real time. The suture tool was guided to approach the object by a dual-camera system. If the tissue inside the tool jaw was inconsistent with the desired suture pattern, a warning message would be generated. The proposed hybrid multilayer perceptron dual-channel convolutional neural network (MLP-DC-CNN) classification platform can automatically classify eight different abdominal tissue types that require different suture strategies for anastomosis. In MLP, numerous handcrafted features (∼1955) were utilized including optical properties and morphological features of one-dimensional (1D) OCT A-line signals. In DC-CNN, intensity-based features and depth-resolved tissues' attenuation coefficients were fully exploited. A decision fusion technique was applied to leverage the information collected from both classifiers to further increase the accuracy. The algorithm was evaluated on 69,773 testing A-line data. The results showed that our model can classify the 1D OCT signals of small bowels in real time with an accuracy of 90.06%, a precision of 88.34%, and a sensitivity of 87.29%, respectively. The refresh rate of the displayed A-line signals was set as 300 Hz, the maximum sensing depth of the fiber was 3.6 mm, and the running time of the image processing algorithm was ∼1.56 s for 1,024 A-lines. The proposed fully automated tissue sensing model outperformed the single classifier of CNN, MLP, or SVM with optimized architectures, showing the complementarity of different feature sets and network architectures in classifying intestinal OCT A-line signals. It can potentially reduce the manual involvement of robotic laparoscopic surgery, which is a crucial step towards a fully autonomous STAR system.

A Study on Dimensionality Reduction and Parameters for Hyperspectral Imagery Based on Manifold Learning.

With the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth's surface objects. However, the abundance of spectral information presents certain challenges for data processing, such as the "curse of dimensionality" leading to the "Hughes phenomenon", "strong correlation" due to high resolution, and "nonlinear characteristics" caused by varying surface reflectances. Consequently, dimensionality reduction of hyperspectral data emerges as a critical task. This paper begins by elucidating the principles and processes of hyperspectral image dimensionality reduction based on manifold theory and learning methods, in light of the nonlinear structures and features present in hyperspectral remote-sensing data, and formulates a dimensionality reduction process based on manifold learning. Subsequently, this study explores the capabilities of feature extraction and low-dimensional embedding for hyperspectral imagery using manifold learning approaches, including principal components analysis (PCA), multidimensional scaling (MDS), and linear discriminant analysis (LDA) for linear methods; and isometric mapping (Isomap), locally linear embedding (LLE), Laplacian eigenmaps (LE), Hessian locally linear embedding (HLLE), local tangent space alignment (LTSA), and maximum variance unfolding (MVU) for nonlinear methods, based on the Indian Pines hyperspectral dataset and Pavia University dataset. Furthermore, the paper investigates the optimal neighborhood computation time and overall algorithm runtime for feature extraction in hyperspectral imagery, varying by the choice of neighborhood k and intrinsic dimensionality d values across different manifold learning methods. Based on the outcomes of feature extraction, the study examines the classification experiments of various manifold learning methods, comparing and analyzing the variations in classification accuracy and Kappa coefficient with different selections of neighborhood k and intrinsic dimensionality d values. Building on this, the impact of selecting different bandwidths t for the Gaussian kernel in the LE method and different Lagrange multipliers λ for the MVU method on classification accuracy, given varying choices of neighborhood k and intrinsic dimensionality d, is explored. Through these experiments, the paper investigates the capability and effectiveness of different manifold learning methods in feature extraction and dimensionality reduction within hyperspectral imagery, as influenced by the selection of neighborhood k and intrinsic dimensionality d values, identifying the optimal neighborhood k and intrinsic dimensionality d value for each method. A comparison of classification accuracies reveals that the LTSA method yields superior classification results compared to other manifold learning approaches. The study demonstrates the advantages of manifold learning methods in processing hyperspectral image data, providing an experimental reference for subsequent research on hyperspectral image dimensionality reduction using manifold learning methods.

Several Stories about High-Multiplicity EFx Allocation (Student Abstract)

Fair division is a topic that has significant social and industrial value. In this work, we study allocations that simultaneously satisfy definitions of fairness and efficiency: EFx and PO. First, we prove that the problem of finding such allocations is NP-hard for two agents. Then, we propose a concept for an ILP-based solving algorithm, the running time of which depends on the number of EFx allocations. We generate input data and analyze algorithm's running time based on the results obtained.

Locally Rainbow Paths

We introduce the algorithmic problem of finding a locally rainbow path of length l connecting two distinguished vertices s and t in a vertex-colored directed graph. Herein, a path is locally rainbow if between any two visits of equally colored vertices, the path traverses consecutively at leaset r differently colored vertices. This problem generalizes the well-known problem of finding a rainbow path. It finds natural applications whenever there are different types of resources that must be protected from overuse, such as crop sequence optimization or production process scheduling. We show that the problem is computationally intractable even if r=2 or if one looks for a locally rainbow among the shortest paths. On the positive side, if one looks for a path that takes only a short detour (i.e., it is slightly longer than the shortest path) and if r is small, the problem can be solved efficiently. Indeed, the running time of the respective algorithm is near-optimal unless the ETH fails.

Incremental information fusion in the presence of object variations for incomplete interval-valued data based on information entropy

Information fusion technology plays a crucial role in integrating data from multiple sources or sensors to generate comprehensive representation, which can eliminate uncertainty in multi-source information systems (Ms-IS). Incomplete interval-valued data, a generalized form of single-valued data, is commonly encountered in real-world scenarios and effectively represents uncertain information. This paper introduces a novel information entropy specifically designed to quantify the uncertainty in incomplete interval-valued data. Based on the proposed entropy, a new unsupervised fusion approach is developed. Additionally, two dynamic update mechanisms are established to obtain fusion results efficiently when collecting new objects and removing obsolete ones. The relevant static and dynamic fusion algorithms are provided, and a detailed analysis and comparison of their time complexities are conducted. Finally, the effectiveness analysis reveals that the proposed method achieves higher average classification accuracy (5% to 8.7% improvement) compared to three common fusion methods (MAXF, MEANF, and MINF), as well as the state-of-the-art entropy-based supervised fusion method (ESF). The efficiency analysis demonstrates that the average running time of dynamic fusion algorithms is significantly lower (66.9% to 85.6% reduction) compared to the static fusion algorithm, and this difference is statistically significant.

Fast peak error correction algorithms for proteoform identification using top-down tandem mass spectra.

Proteoform identification is an important problem in proteomics. The main task is to find a modified protein that best fits the input spectrum. To overcome the combinatorial explosion of possible proteoforms, the proteoform mass graph and spectrum mass graph are used to represent the protein database and the spectrum, respectively. The problem becomes finding an optimal alignment between the proteoform mass graph and the spectrum mass graph. Peak error correction is an important issue for computing an optimal alignment between the two input mass graphs. We propose a faster algorithm for the error correction alignment of spectrum mass graph and proteoform mass graph problem and produce a program package TopMGFast. The newly designed algorithms require less space and running time so that we are able to compute global optimal alignments for the two input mass graphs in a reasonable time. For the local alignment version, experiments show that the running time of the new algorithm is reduced by 2.5 times. For the global alignment version, experiments show that the maximum mass errors between any pair of matched nodes in the alignments obtained by our method are within a small range as designed, while the alignments produced by the state-of-the-art method, TopMG, have very large maximum mass errors for many cases. The obtained alignment sizes are roughly the same for both TopMG and TopMGFast. Of course, TopMGFast needs more running time than TopMG. Therefore, our new algorithm can obtain more reliable global alignments within a reasonable time. This is the first time that global optimal error correction alignments can be obtained using real datasets. The source code of the algorithm is available at https://github.com/Zeirdo/TopMGFast.

Efficient secure channel free identity-based searchable encryption schemes with privacy preserving for cloud storage service

Cloud storage is a basic service model of the cloud computing. Since the cloud data is stored in the ciphertext for the data confidentiality, how to search the cloud data again in ciphertext state for users is a natural requirement. The searchable encryption (SE) gives an efficient solution to achieve both the data confidentiality and the searchable requirement simultaneously. In SE schemes, the user can transfer a search trapdoor to the cloud server from a secure channel and the cloud server can use the received trapdoor to search the corresponding keyword ciphertext. Since the keywords are with low entropy, the traditional SE is vulnerable to keyword guessing attack. In order to remove the need of the secure channel and also to achieve the security against the keyword guessing attack, we build a single-user identity-based secure channel free SE scheme in the random oracle model by using lattice-based tools. Only the designated cloud server can finish the ciphertext search which means the secure channel between the user and the cloud server is not needed in the proposed scheme. Under the hardness of the learning with errors problem, we prove that the proposed scheme is ciphertext indistinguishable under the selective identity and chosen keyword attacks. Moreover, the proposed scheme also satisfies the trapdoor indistinguishability which directly leads to the security against the outside offline keyword guessing attack. Furthermore, we extend the proposed single-user scheme into the multi-user scenario. The proposed multi-user scheme inherits all functions achieved in the single-user scheme, such as secure channel free. Meanwhile, ciphertext length is fixed with the number of users increasing, which is more suitable for the large group users. In addition, we analyze the theoretical evaluation and experimental evaluation between the proposed schemes and some known literatures respectively. The results demonstrate that our proposed algorithms have several advantages in the both single-user and multi-user schemes, for example, the ciphertext lengths in the single/multi-user schemes are only 5.632KB and 6.016KB respectively and the running time of Test algorithm for any user groups is fixed to be 0.65ms in our simulated experiments.

Parameterized Algorithm for the Poset Cover Problem

It is already known that the 1-Poset and 2-Poset Cover Problems are in 𝑷. In this paper, we extended the previous results and devised an algorithm for the 𝒌-Poset Cover Problem, for any 𝒌 number of posets that cover the input. The algorithm runs in 𝑶(𝒎2k 𝒏2), where 𝒎 and 𝒏 are the input size. With this running time, we can say that the problem belongs to XP (slicewise polynomial). The algorithm runs efficiently for small fixed 𝒌 but runs exponentially for large 𝒌. While the algorithm running time has yet not to be efficient for large 𝒌, we have shown a significant improvement from a brute-force solution, which runs in 2𝒎 𝒏2 + 𝑶(�𝒌 𝒊 � 1 2𝒎𝒊𝒏) - exponential even for small fixed 𝒌.