Restructure blogs as Astro monorepo

sites/puzzles/src/content/research/paper-review-approximation.md

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+---
+title: "Understanding the Latest Approximation Algorithm for Set Cover"
+description: "A detailed walkthrough of a breakthrough approximation algorithm with practical implications."
+pubDate: "Feb 15 2024"
+image: "https://images.unsplash.com/photo-1516321318423-f06f85e504b3?w=400&auto=format&fit=crop&q=60"
+authorImage: "/avatar/avatar1.png"
+authorName: "Neeldhara"
+---
+
+# Understanding the Latest Approximation Algorithm for Set Cover
+
+A recent paper achieves a breakthrough in the Set Cover problem, improving the approximation ratio while maintaining practical runtime.
+
+## The Algorithm
+
+The approach combines local search with a clever LP rounding scheme. The dual interpretation provides beautiful geometric insights.
+
+## Why This Matters
+
+Set Cover appears everywhere - from facility location to machine learning feature selection. This improvement has immediate practical impact.
+
+## Implementation Details
+
+The paper's theoretical elegance translates surprisingly well to practice. Key optimizations include:
+- Lazy evaluation of set intersections
+- Incremental updates to the LP solution
+- Smart caching strategies
+
+## Future Work
+
+The techniques here might extend to weighted variants and online settings.