With the rapid development of social network applications, social network has become an important medium for people to interact. For the minimum distance computation of all pairs in networks, Alon N[4] proposed an algorithm with matrix multiplication, combining with distance product association law and block matrix multiplication, all pairs shortest path length algorithm on networks has time bound O((2n^3)/B logn). In practical applications, considering the scale-free characteristics of social networks and the precision limitations of floating-point operations on computer hardware, I found that the shortest path algorithm has an improved time bound O((14n^3)/B). Based on the above theory, I propose an all pairs shortest path algorithm that combines sparseness judgment and convergence judgment, leveraging the distance product algorithm with matrix multiplication, distance product association law, block matrix multiplication, scale-free characteristics of social networks, and limitation of floating-point operations on hardware. Testing on a social network dataset with 8508 actors, compared to Alon N algorithm, proposed algorithm has a performance improvement of 39% to 36.2 times on CPU and GPU.

中文翻译：

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社交网络所有对最短路径中矩阵乘积收敛率的下界

随着社交网络应用的快速发展，社交网络已经成为人们进行交互的重要媒介。对于网络中所有对的最小距离计算，Alon N[4]提出了一种矩阵乘法算法，结合距离积关联律和块矩阵乘法，网络上所有对最短路径长度算法的时间界限为O((2n^ 3)/B 登录)。在实际应用中，考虑到社交网络的无标度特性以及浮点运算在计算机硬件上的精度限制，我发现最短路径算法具有改进的时间界O((14n^3)/B)。基于上述理论，我提出了一种结合稀疏判断和收敛判断的全对最短路径算法，利用具有矩阵乘法的距离积算法、距离积关联律、块矩阵乘法、社交网络的无标度特性以及硬件上浮点运算的限制。在具有 8508 个参与者的社交网络数据集上进行测试，与 Alon N 算法相比，该算法在 CPU 和 GPU 上的性能提升了 39% 至 36.2 倍。