Work on finding algorithms for the longest path (aka critical path) in cyclic directed graphs. The general case is NP, but what algorithms can you come up with

Work on finding algorithms for the longest path (aka critical path) in cyclic directed graphs. The general case is NP, but what algorithms can you come up with for specific graphs? How much could you brute force with a massive computing power? Edit: been working on this on and off for the past few years. A very fun problem. Also recommendation algorithms are another fun problem that you want to toss hardware at.