The sorting algorithms have found applications in various research fields including image and video processing. High speed sorting is important in real-time applications, such as real-time image processing. Two properties are criterion for sorting networks: the number of steps (speed) and the number of comparators (efficiency). In this paper, we have proposed a method to decrease the number of steps. We introduce a new method for sorting an unordered sequence, which is based on the graph theory concept,and contrary to the conventional sorting networks, it consists of graph edge calculators rather than compare-and-swaps. An outstanding feature of the proposed method is that for small number of inputs, its number of steps is independent of the number of inputs that denotes it orders N inputs in O(1) steps. Moreover, the proposed method surpasses the previous ones in term of speed; it just needs two steps to sort a sequence. In the first step, all the inputs are compared with each other, and in the second step, the results of comparisons direct the inputs to the right outputs. To justify the functionality, the proposed method is simulated with the Modelsim-Altera and implemented on a Cyclone IV FPGA platform. Simulation results indicate that in comparison with the Bather's Bitonic mergesort, which is known to be the fastest algorithm, the proposed method while requires 80% more LEs, consumes 52% less memory and achieves 73% more throughput. Furthermore, the Bitonic mergesort can only accept a power of 2 number of inputs, while the proposed method does not hold such a limitation.

排序算法已在包括图像和视频处理在内的各种研究领域中找到了应用。高速分类在实时应用（例如实时图像处理）中很重要。排序网络的标准有两个属性：步数（速度）和比较器数（效率）。在本文中，我们提出了一种减少步骤数的方法。我们引入了一种基于图论的概念对无序序列进行排序的新方法，与传统的排序网络相反，它由图边缘计算器而不是比较和交换组成。该方法的一个突出特点是对于少量输入，其步数与输入数无关，这表示它在O（1）中对N个输入进行排序脚步。此外，该方法在速度上超过了以前的方法。它只需要两个步骤就可以对序列进行排序。第一步，将所有输入相互比较，第二步，比较结果将输入定向到正确的输出。为了证明其功能合理性，所提出的方法用Modelsim-Altera进行了仿真，并在Cyclone IV FPGA平台上实现。仿真结果表明，与已知的最快算法Bather的Bitonic mergesort相比，该方法所需的LE数量增加80％，内存消耗减少52％，吞吐量提高73％。此外，Bitonic mergesort只能接受2个输入的幂，而所提出的方法没有这种限制。