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deepmind.google·6d ago
AI Engineering
Hacker News·Aug 21·5 min read
Hacker News·Aug 21·5 min readAnother Better Lower Bound for N=17 Square Packing
TL;DR
A new lower bound for packing 17 unit squares has been established, showing that s(17) is at least 4.5058. This builds on previous findings and refines the understanding of square packing arrangements.
✦ Why It Matters
Consider exploring new packing algorithms that leverage this improved lower bound for efficiency.
Key Takeaways
- Review the new packing strategy for potential applications.
- Explore linear programming techniques for optimization tasks.
- Consider the implications for packing larger numbers of squares.
- Investigate the geometric arrangements used in the new bound.
How It Works
The new lower bound of 4.5058 was derived by selecting 168 points in a 29x29 grid, where each point has a specific weight. The arrangement ensures that any configuration of 17 unit squares must overlap with these points, thus establishing a lower limit on the size of the enclosing square.
The use of linear programming allowed for systematic testing of various configurations, optimizing the arrangement to minimize the enclosing square's size.