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

Lower Bounds on Rate of Convergence of Matrix Products in All Pairs Shortest Path of Social Network