  Gaussian Boson sampling (GBS) plays a crucially important role in
demonstrating quantum advantage. As a major imperfection, the limited
connectivity of the linear optical network weakens the quantum advantage result
in recent experiments. Here we present a faster classical algorithm to simulate
the GBS process with limited connectivity. In this work, we introduce an
enhanced classical algorithm for simulating GBS processes with limited
connectivity. It computes the loop Hafnian of an $n \times n$ symmetric matrix
with bandwidth $w$ in $O(nw2^w)$ time which is better than the previous fastest
algorithm which runs in $O(nw^2 2^w)$ time. This classical algorithm is helpful
on clarifying how limited connectivity affects the computational complexity of
GBS and tightening the boundary of quantum advantage in the GBS problem.
