I just wrote a blog post about a graph problem I finally solved after being stuck on it since 2021 (link below). Three takeaways:
1. My favorite part of writing blog posts now, rather than research papers, is that I can include a "Backstory" section talking about how I got interested in the problem in the first place. I wish research papers had this section.
2. The write-up got a lot clearer simply from renaming "path 1" and "path 2" to "red path" and "blue path". This allows me to say things like "red edge" instead of "edge in P1", and it removes a level of subindices (e.g., e1_i and e2_i become r_i and b_i).
3. Something that was very helpful in having a breakthrough now vs 2021 was vibe coding a tool to visualize the graphs (see screenshot). Yes, I could have coded the visualization tool myself back then, but vibe coding removed the friction. Ironically, vibe coding has a rep for only being good at starting projects and then abandoning them, but here it helped me pick up an abandoned project and finish it.
