In population genetics, **Kinship matrix** is a relatedness matrix, which can be used to measure the degree of relationship between any of two related individuals. Suppose there are **n **individuals, and each individual is represented explicitly by a node of pedigree tree or by a large number of genotypic markers(m). The kinship matrix **K** is a 2D matrix with the dimension of ** nxn **. We can use the genotypic markers to generate a kinship matrix and its calculation is a very critical step in ** genome-wide association studies (GWAS)**. Here, the kinship matrix entry ** K(i,j)** is a coefficient to assess the genetic resemblance between individual **i** and individual **j**. Consider the symmetry, the kinship matrix is a diagonal matrix. Such Kinship matrix is called the **main effect (1D)** kinship matrix, which is compared to our defined **2D epistatic effect(marker pair) ** kinship matrix.

Recently, high-throughput sequencing, particularly **NGS** technology make it capable of sequencing and discovering a massive number of **SNPs** and furtherly explore the within-species diversity via constructing **haplotype maps** and conducting **(GWAS)**. A typical **GWAS** study may need to call ** millions** scale SNPs, and the genotypic markers. The kinship matrix calculating, as the first step of **GWAS** study, requires **loading the massive genotypic data** at first and then compute **pair-wise** individuals' relatedness. Therefore, the kinship matrix calculation essentially is very **time-consuming**, especially when the individual number amount to ** several thousands ** and the genotypic marker number reach to **several millions**.

In the recent years, **GPU (Graphics Processing Units)** with multiple hardware processor (>1,000) cores has become a standard **HPC (High Performance Computing) **solution system for large scale computing, e.g., large scale **matrix operation**.

We have analyzed the math principle and the complexity of the marker-assist kinship matrix, and successfully developed this **GPU** empowered pipeline, **KMC1D**, for **main effect** kinship matrix calculating. Briefly, we first divide the ultra-high-dimensional **markers ** into successive **blocks**. We then calculate the kinship matrix for **each block** and merge the **block-wise** kinship matrices to form the genome-wide kinship matrix. All the matrix operations have been **parallelized ** using **GPU** kernels on our **NVIDIA** GPU-accelerated server platform. Our performance analyses show that the calculation of **KMC1D** can achieve speed acceleration by hundreds of times over the conventional **CPU-based** computing.

The users are required to upload one kind of **genotype matrix **file for computing one of two main kinship matrix, e.g. **additive**, or **dominance**

Also, to assist in transmitting **large-size** genotype matrix file, we implemented a "resumable multithreading-chunked uploading" function for **HTML5-compatible browsers**

To calculate the **epistatic effect 2D **kinship matrix, you may use our other GPU pipeline **KMC2D**.

**Reference**

**1.** Xu, S., "Mapping Quantitative Trait Loci by Controlling Polygenic Background Effects". Genetics, 2013. 195(4):p.1709-23.

**2.** Zhang W., Dai X., Wang Q., Xu S., Zhao P.X., "PEPIS: A Pipeline for Estimating Epistatic Effects in Quantitative Trait Locus Mapping and Genome-Wide Association Studies", 2016. PLoS Comput Biol, 12(5)

**3.** Cecilia J. M. , Garc´ıa J. M. , and Ujaldon M., “The GPU on the Matrix-Matrix Multiply: Performance Study and Contributions”, in Parallel Computing: From Multicores and GPU’s to Petascale, B. Chapman et al., Eds. Advances in Parallel Computing, vol. 19, pp. 331-340, 2010.

**4.** Dobravec T., Bulic P., "Comparing CPU and GPU Implementations of a Simple Matrix Multiplication Algorithm", IJCEE, vol 9, 430-438, 2017.