Row Major Order Research Articles

Optimized Parallel Sorting of 2D Arrays Using Row-Major Division and Final Merging Strategy

In this paper, we present a novel approach to sorting 2D arrays that leverages row-major order partitioning followed by a single, parallelized merging stage. We demonstrate how this method optimizes cache usage and reduces overhead in high-performance computing environments. Our results indicate significant performance improvements compared to traditional parallel sorting techniques, particularly in large-scale datasets

LMSFC: A Novel Multidimensional Index Based on Learned Monotonic Space Filling Curves

The recently proposed learned indexes have attracted much attention as they can adapt to the actual data and query distributions to attain better search efficiency. Based on this technique, several existing works build up indexes for multi-dimensional data and achieve improved query performance. A common paradigm of these works is to (i) map multi-dimensional data points to a one-dimensional space using a fixed space-filling curve (SFC) or its variant and (ii) then apply the learned indexing techniques. We notice that the first step typically uses a fixed SFC method, such as row-major order and z -order. It definitely limits the potential of learned multi-dimensional indexes to adapt variable data distributions via different query workloads. In this paper, we propose a novel idea of learning a space-filling curve that is carefully designed and actively optimized for efficient query processing. We also identify innovative offline and online optimization opportunities common to SFC-based learned indexes and offer optimal and/or heuristic solutions. Experimental results demonstrate that our proposed method, LMSFC, outperforms state-of-the-art non-learned or learned methods across three commonly used real-world datasets and diverse experimental settings.

Power System Connectivity Visualization Using an Orthogonal Graph Layout Algorithm Based on the Space-Filling Technique

In this study, a novel orthogonal graph layout algorithm was proposed to efficiently represent the connection relationship between each node in power system data. The proposed layout algorithm is a four-stage algorithm. First, clustering was performed based on the connection relationship between nodes, and the obtained clusters were placed close to squares by using the squarified treemap technique to fully utilize the given space. Next, adjacent nodes were arranged in a snakelike order in each cluster according to the characteristics of the IEEE test system data. The links were then arranged according to the positional relationship of the pairs of connected nodes. Each node had several ports so that links could be distributed evenly according to the direction of the links. A case in which all nodes were arranged orthogonally in an arbitrary manner without performing clustering; a case in which adjacent nodes within each cluster were arranged in arbitrary order after only performing clustering; and a case where adjacent nodes within each cluster were arranged in row-major order after only performing clustering were compared. The results revealed that the proposed method considerably improved edge crossing, edge bending, and edge length.

Secured image steganography based on Catalan transform

Transform domain steganography methods are always preferable than spatial domain methods to the research community due to following advantages: better feature identification, improved security and higher robustness. In this paper, an integer sequence named Catalan Transform (CT) has been exploited in the image steganography domain. At the outset, the cover image is decomposed into 2 × 2 non-overlapping blocks in row major order. Then, each such block i.e., 4-pixel group is converted into transform domain using CT. Secret bits are embedded into the transformed components in varying proportions which facilitates us to achieve a payload in the range of 1 to 4 bpp. Inverse Catalan Transform (ICT) is applied over transformed cum embedded quadruples to generate the stego-pixels in spatial domain. Successive embedding operation over an entire image ensures the formation of stego-image. Experimental results confirm that the Peak Signal to Noise Ratio (PSNR) values obtained by the proposed method are always above the acceptable level (i.e., 30 dB) and at the same time, it outperforms many state-of-the-art methods. Other metrics such as Mean Squared Error (MSE), Structural Similarity Index Measure (SSIM), Normalized Cross Correlation (NCC) and Global histograms with similarity measure have also been computed which prove the effectiveness of the proposed scheme. The robustness of the stego-images has further been tested using the StegExpose tool and it is found that the tool is unable to detect the presence of secret data. The code of this work is available at: https://github.com/Souradeep150/Catalan-based-Steganography .

Design and Implementation of LSB based Minimum Deviation Steganography technique on High Payload Grayscale Images

The paper discusses the design of a new steganographic method for 8-bit grayscale images. Here, the input cover image is decomposed into 2 × 2 blocks of pixels which are non-overlapping in row major order. Each block can embed 7- bits from secret bit-stream. Successive block embedding operation ensures the concealment of the entire hidden information into the carrier image. The proposed method offers a fixed payload of 1.75 bits per pixel (bpp) which is considered to be a high payload in the field of Steganography. The degradation of the stego-image is also not severe in our method and that can be analyzed by observing the Peak Signal to Noise Ratio (PSNR) of greater than 30 dB. In the reverse way, the receiver decomposes the cover image into 2 × 2 non-overlapping blocks of pixels in row major order. Successive extraction of 7- secret bits from each block ensures the re-generation of the secret information. Simulation results ensure that the proposed method is superior than other schemes in terms of qualitative clarity of the Stego-image.

On the use of the Stirling Transform in image steganography

Stirling Transform (ST) is primarily used in combinatorial mathematics to convert a polynomial sequence of n non-negative integers into another integer sequence. The source sequence can also be re-generated from the target sequence based on the principle of inverse Stirling Transform (IST). This property is considered as an interesting study and has been exploited for steganography in digital images. In this paper, the cover image is decomposed into the pair (n = 2) of neighboring pixel components in row major order. Stirling Transform (ST) converts the pair of pixel components into the pair of transformed components corresponding to red, green and blue channels. The obtained transformed components are always non-negative, which fabricates varying sizes of the secret image based on the specified payload in the range of 0.5 to 3 bpB (bits per Byte). To address the security issue, the secret image is scrambled through a simple scrambling process prior to embedding. The pixel adjustment process ensures the non-occurrence of overflow/underflow during embedding. Inverse Stirling Transform (IST) re-computes the pair of pixel components from the embedded pair of transformed components. This process is repeated till the secret information is concealed and the stego-image is produced. At the recipient end, the reverse procedure is applied to extract the concealed information from the stego-image based on the following parameters: shared PIN, system time and the one time password (OTP). Message digest obtained through MD5 algorithm is used to verify the authenticity. Simulation results ensures that the proposed scheme outperforms Chang et al.’s [17], Xia et al.’s [18], 3-LSB [2] and hybrid GEMD [7] schemes in terms of image quality with respect to increasing payloads.

Improved exploiting modification direction‐based steganography using dynamic weightage array

An improved exploiting modification direction-based image steganography technique has been proposed. The cover image is decomposed into non-overlapping units of n pixels each to embed 2 kn -ary numbers in row major order. Here, k is the number of bits to be embedded in each pixel. Therefore, the number of bits the message sender wants to embed is not restricted by this method. The dynamic nature of the weightage array makes the process pseudo-random by producing a different key for different message images. Experimental results ensure higher payload and reduced quality distortion of stego-images over existing schemes.

OpenMP, OpenMP/MPI, and CUDA/MPI C programs for solving the time-dependent dipolar Gross–Pitaevskii equation

We present new versions of the previously published C and CUDA programs for solving the dipolar Gross-Pitaevskii equation in one, two, and three spatial dimensions, which calculate stationary and non-stationary solutions by propagation in imaginary or real time. Presented programs are improved and parallelized versions of previous programs, divided into three packages according to the type of parallelization. First package contains improved and threaded version of sequential C programs using OpenMP. Second package additionally parallelizes three-dimensional variants of the OpenMP programs using MPI, allowing them to be run on distributed-memory systems. Finally, previous three-dimensional CUDA-parallelized programs are further parallelized using MPI, similarly as the OpenMP programs. We also present speedup test results obtained using new versions of programs in comparison with the previous sequential C and parallel CUDA programs. The improvements to the sequential version yield a speedup of 1.1 to 1.9, depending on the program. OpenMP parallelization yields further speedup of 2 to 12 on a 16-core workstation, while OpenMP/MPI version demonstrates a speedup of 11.5 to 16.5 on a computer cluster with 32 nodes used. CUDA/MPI version shows a speedup of 9 to 10 on a computer cluster with 32 nodes.

Binomial transform based fragile watermarking for image authentication

In this paper, a novel Binomial transform based fragile watermarking technique has been proposed for color image authentication. Binomial transform (BT) is applied to convert each 2 × 2 sub-image block into transform domain in row major order. On average, two bits of authenticating watermark are fabricated on each transformed component starting from the least significant bit position (LSB-0). Inverse Binomial transform (IBT) is performed as post-embedding operation to convert each 2 × 2 transformed block back into the spatial domain. A delicate re-adjustment is performed on the first embedded component to keep the pixel components positive and less than or equal to 255 keeping the fabricated watermark unaltered. The watermark is extracted at the recipient end based on the reverse operation and is verified for authentication using a message digest. Experimental result ensures that the proposed technique obtain higher Payload and Peak Signal to Noise Ratio (PSNR) as compared to existing methods.

Binomial Transform Based Image Authentication (BTIA)

In this paper, a fragile watermarking technique based on Binomial transform (BT) has been proposed for color image authentication (BTIA). An initial adjustment is applied to adjust the pixel values. The Binomial transform (BT) is applied to convert each pair of pixel components into transform domain in row major order. Two bits of the authenticating watermarks, starting from the least significant bit position are embedded into each component of transformed pair. A post-embedding adjustment has also been incorporated to keep the embedded component values closest to the original without hampering the embedded watermark bits. The inverse Binomial transform (IBT) is applied on each adjusted pair to regenerate the pixel components which successively produce the watermarked image. At the receiving end, the whole watermark can be extracted by the reverse procedure which can be verified for authentication by obtaining a message digest. Experimental results conform that the proposed technique offers a higher payload and PSNR over existing techniques [7, 9].

A Genetic Algorithm based Steganography Using Discrete Cosine Transformation (GASDCT)

Abstract In this paper a Genetic Algorithm based steganographic technique in frequency domain using discrete cosine transform has been proposed. A 2×2 sub mask of the source image is taken in row major order and Discrete Cosine Transformation is applied on it to generate four frequency components. Two bits of the authenticating image are embedded into each transformed coefficients except the first one. In each coefficient second and third positions from LSB are chosen for embedding in the transform domain. Stego sub intermediate image is generated through reverse transform. Sub mask from this intermediate image is taken as initial population. New Generation followed by Crossover is applied on initial population to enhance a layer of security. New Generation is applied to initial population. Rightmost three bits of each byte are taken, a consecutive bitwise XOR is applied on it in three steps which generates a triangular form. The first bit of each intermediate step is taken as the output and Crossover is performed on two consecutive pixels where two LSB bits of two consecutive bytes are swapped. The dimension of the hidden image is embedded followed by the content. Reverse process is followed during decoding. The proposed scheme obtains high image fidelity, PSNR and high capacity of embedding in stego images compared Chang Chin et al. [1] .

Stirling Transform based Color Image Authentication

In this paper, a fragile watermarking technique based on Stirling transform (ST) has been proposed to authenticate color images (STCIA). The pixel components of the cover/carrier image are adjusted prior to embedding, if necessary. Stirling transform (ST) is used to convert each pair of pixel components into transformed pair in row major order. Two bits of the watermark starting from the least bit position are embedded. A post-embedding adjustment has also been incorporated to keep the embedded components closest to the original without hampering the fabricated watermark bits. Inverse Stirling transform (IST) is appli ed on each adjusted pair to obtain the watermarked image. The recipient extracts the whole watermark through reverse procedure which in turn may be verified for authentication by ensuring the integrity of the re-generated message digest. Experimental results conforms that the proposed technique has been improvised in terms of payload and PSNR over existing techniques [13] , [14] .

An Image Authentication Technique in Frequency Domain using Genetic Algorithm (IAFDGA)

In this paper Genetic Algorithm based image authentication technique in frequency domain using Z transformation (IAFDGA) has been proposed.A 2×2 mask is taken from the source image in row major order. Z transformation is applied to transform it into freque ncy domain. Six bits are embedded in each sub mask into the second and third transformed coefficients. The sub mask is then transformed into spatial domain using inverse Z transform. Embedded image mask of size 32 bits are taken as initial population. New Generation followed by Crossover and Mutation are applied on it.To obtain New Generation , minimum coefficient of the mask is chosen, if the minimum coefficient is negative then subtract the minimum coefficient from each coefficient of the mask so that ex traction of hidden bits are ensured. For the Crossover operation consecutive bit -wise XOR is performed on the rightmost three bits of each byte in three steps. It will form a triangular form and the first bit of each step is taken as the output. Right most two LSBs of two consecutive pixels are swapped with each other as a part of Mutation operation. Genetic algorithm is applied to enhance a layer of security level. At the time of embedding dimension of the authenticating image followed by the content are e mbedded. Reverse process is followed at the time of extraction. High PSNR obtained for various images compared to existing Chin -Chen Chang et al.[2] conform the quality of invisible watermark IAFDGA. Large capacity as compared to existing algorithm [1] ensured the high payload of the scheme.

Steganographic Technique in Z-Domain for Image Authentication (STZ-DIA)

This paper deals with a novel technique for image authentication in Z-domain based on the Discrete two dimensional Z-Transform. The Z-Transform is exploits on sub-image block called mask of size 2 x 2 for frequency components of the corresponding spatial component in row major order. Multimedia Image authentication is done by hiding secret message/image into the real part of the component obtained by discrete two dimensional Z-Transform of the carrier image. A single bit from the authenticating image/message is embedded in middle and low quantum value of carrier image mask. Robustness is achieved through embedding bits in variable positions of carrier image determined by the decimal value of sum of higher three bits of frequency values (i.e. b7+b6+b5). After embedding, a delicate re-adjust phase is incorporated in all frequency components of each mask, to keep the pixel values positive and non-fractional in the spatial domain. The invisibility is conformed by using delicate re-adjust phase. This technique is also applicable for secrete data transmission through carrier color image by hiding secrete data. Experimental results show the robustness and performance of the proposed watermarking technique. Keywords: Z-Transform, Inverse Z-Transform, DFT, QFT, DCT

Watermarking in Transform Domains (WTD)

In this paper two separate models of watermarking has been proposed based on wavelet and Z domain along with comparative study in terms of PSNR, MSE and IF. The cover image is passed through transformation based on 2 x 2 mask as sliding window manner in row major order to convert the spatial components of cover image into frequency coefficients. Four bits of authenticating image pixels are embedded into transform coefficients of each mask as watermark of the scheme to achieve the payload of one bpB (bit per Byte). Extraction is made in reverse manner. Results are computed and compared between two steganographic models in terms of Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), and Image Fidelity (IF) which show better performances in Z-domain with enhanced fidelity.

Steganographic Technique for High Volume Secrete Data Transmission through Colour Image (STHVSDTCI)

This paper presents a novel steganographic technique which demonstrates the secrete data transmission technique through colour image in frequency domain based on the Discrete Fourier Transformation (DFT) which pertain to colour image authentication. Secrete transmission is done by hiding secrete message/secrete image into the transformed frequency component of source image. The DFT is applied on sub-image block called mask of size 2 x 2 in row major order. Three secrete message/image bits are fabricated within the transformed real frequency component of each source image byte except the LSB of first frequency component of each mask. After embedding, a delicate readjust phase is incorporated in all the frequency component of each mask, to keep the quantum value positive and non fractional in spatial domain. Robustness is achieved by hiding an authenticating or secretes message/image in the frequency component with both positive and negatives quantum values and invisibility is satisfied in spatial domain using delicate re-adjust phase. Inverse DFT (IDFT) is performed as final steps after embedding to transform embedded image in frequency domain to spatial domain. Experimental results conformed that the proposed algorithm performs better than discrete cosine transformation (DCT), Quaternion Fourier Transformation (QFT) based scheme and Spatio Chromatic DFT (SCDFT). Keywords: QFT, DFT, IDFT, DCT, MD and SCDFT

A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves

We develop a novel construction method forn-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. Ann-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing ann-dimensional Hilbert space-filling curve. The tensor product formulation ofn-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas ofn-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.

A Novel Technique for Image Authentication in Frequency Domain Using Discrete Fourier Transformation Technique (IAFDDFTT)

In this paper a novel technique for Image Authentication in Frequency Domain using Discrete Fourier Transformation Technique (IAFDDFTT) has been proposed to authenticate a gray level PGM, TIFF image by embedding a message/image where 2 x 2 submatrix is taken as source matrix from the image matrix and transform into the frequency domain. Two bits of authenticating message/image are fabricated within the real part of each pixel, excluding the first pixel of each submatrix where the position is chosen using a hash function. The process is repeated for each submatrix on row major order to insert authenticating message/image content and 128 bits Message Digest (MD-5), generated from authenticating message/image. Inverse DFT is performed to transform the embedded image from frequency to spatial domain as final step of encoding. The decoding is done through the reverse procedure. The experimental results against statistical and visual attack has been discussed and compared with the existing steganography algorithm like S-Tools. Histogram analysis, noise analysis, and standard deviation computation of source image with embedded image shows the better results in comparison with existing S-Tools.

Some P-RAM Algorithms for Sparse Linear Systems

PRAM algorithms for Symmetric Gaussian elimination is presented. We showed actual testing operations that will be performed during Symmetric Gaussian elimination, which caused symbolic factorization to occur for sparse linear systems. The array pattern of processing elements (PE) in row major order for the specialized sparse matrix in formulated. We showed that the access function in2+jn+k contains topological properties. We also proved that cost of storage and cost of retrieval of a matrix are proportional to each other in polylogarithmic parallel time using P-RAM with a polynomial numbers of processor. We use symbolic factorization that produces a data structure, which is used to exploit the sparsity of the triangular factors. In these parallel algorithms number of multiplication/division in O(log3n), number of addition/subtraction in O(log3n) and the storage in O(log2n) may be achieved.

Compressing table data with column dependency

Tables are two-dimensional arrays given in row-major order. Such data have unique features that could be exploited for effective compression. For example, tables often represent database files with rows as records so certain columns or fields in a table may have few distinct values. This means that simply transposing the data can make it compress better. Further, a large source of information redundancy in a table is the correlation among columns representing related types of data. This paper formalizes the notion of column dependency as a way to capture this information redundancy across columns and discusses how to automatically compute and use it to substantially improve table compression.