Finding all the Lower Boundary Points in a Multistate Two-Terminal Network

System reliability of a multistate flow network can be computed in terms of all the lower boundary points, called <italic>d</italic>-minimal paths (<inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula>-MPs). Although several algorithms have been proposed in the literature for the <inline-formula><tex-math notation="LaTeX"> $d$</tex-math></inline-formula>-MP problem, there is still room for improvement upon its solution. Here, some new results are presented to improve the solution of the problem. A simple novel algorithm is improved to solve a Diophantine system that appeared in the <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula>-MP problem. Then, an improved algorithm is proposed for the <inline-formula><tex-math notation="LaTeX">$d$</tex-math> </inline-formula>-MP problem. It is also explained how the proposed algorithm can be used in order to assess the reliability of some smart grid communication networks. We provide the complexity results and show the main algorithm to be more efficient than the existing ones in terms of execution times through some benchmark networks and a general network example. Moreover, we compare the algorithms through one thousand randomly generated test problems using the Dolan and Moré's performance profile.