In general, subset sum problem is strongly believed to be computationally difficult to solve. But in 1983, Lagarias and Odlyzko proposed a probabilistic algorithm for solving subset sum problems of sufficiently low density in polynomial time. In 1991, Coster et. al. improved the Lagarias-Odlyzko algorithm and solved subset sum problems with higher density. Both algorithms reduce subset sum problem to finding shortest non-zero vectors in special lattices. In this thesis, we first proposed a new viewpoint to define the problems which can be solved by this two algorithms and shows the improved algorithm isn't always better than the Lagarias-Odlyzko algorithm. Then we verify this notion by experimentation. Finally, we find that the Lagrias-Odlyzko algorithm can solve the high-density subset sum problems if the weight of solution is higher than 0.7733n or lower than 0.2267n, even the density is close to 1.