We propose a new alignment-free algorithm by constructing a compact vector representation on $\mathbb{R}^{24}$ of a DNA sequence of arbitrary length. Each component of this vector is obtained from a representative sequence, the elements of which are the values realized by a function $\Gamma$. $\Gamma$ acts on neighborhoods of arbitrary radius that are located at strategic positions within the DNA sequence and carries complete information about the local distribution of frequencies of the nucleotides as a consequence of the uniqueness of prime factorization of integer. The algorithm exhibits linear time complexity and turns out to consume significantly small memory. The two natural parameters characterizing the radius and location of the neighbourhoods are fixed by comparing the phylogenetic tree with the benchmark for full genome sequences of fish mtDNA datasets. Using these fitting parameters, the method is applied to analyze a number of genome sequences from benchmark and other standard datasets. The algorithm proves to be computationally efficient compared to Co-phylog and CD-MAWS when applied over a certain range of a simulated dataset.

翻译：我们提出一种新的免比对算法，通过构建DNA序列在$\mathbb{R}^{24}$上的紧凑向量表示（适用于任意长度序列）。该向量的每个分量均源于代表性序列，其元素由函数$\Gamma$的取值决定。$\Gamma$作用于DNA序列中位于战略位置的任意半径邻域，并凭借整数质因数分解的唯一性，完整编码了核苷酸局部频率分布信息。该算法具有线性时间复杂度，且内存消耗极低。通过将系统发育树与鱼类线粒体DNA全基因组数据集基准进行比对，确定了表征邻域半径与位置的两个自然参数。利用这些拟合参数，该方法被应用于分析来自基准及其他标准数据集的多个基因组序列。实验表明，在模拟数据集的特定范围内，该算法相较于Co-phylog和CD-MAWS具有更高的计算效率。