Struggling to Optimize a Recursive Algorithm's Time Complexity Beyond O(n log n) - Any Brilliant Ideas?

I'm working on a complex graph traversal problem where my current recursive solution consistently lands at O(n log n). I'm positive a linear O(n) approach exists, but every attempt with memoization or iterative conversion introduces new complexities that don't quite get me there. I'm hitting a wall and desperately need fresh perspectives on how to break through this performance barrier. What strategies or patterns might I be overlooking?