An undergraduate student, Noah Stephens-Davidowitz, has disproven a longstanding conjecture in computer science related to hash tables. He demonstrated that "linear probing," a simple hash table collision resolution method, can achieve optimal performance even with high load factors, contradicting a 40-year-old assumption. His work not only closes a theoretical gap in our understanding of hash tables but also introduces a new, potentially faster type of hash table based on "robin hood hashing" that could improve performance in databases and other applications.
The blog post showcases efficient implementations of hash tables and dynamic arrays in C, prioritizing speed and simplicity over features. The hash table uses open addressing with linear probing and a power-of-two size, offering fast lookups and insertions. Resizing is handled by allocating a larger table and rehashing all elements, a process triggered when the table reaches a certain load factor. The dynamic array, built atop realloc, doubles in capacity when full, ensuring amortized constant-time appends while minimizing wasted space. Both examples emphasize practical performance over complex optimizations, providing clear and concise code suitable for embedding in performance-sensitive applications.
Hacker News users discuss the practicality and efficiency of Chris Wellons' C implementations of hash tables and dynamic arrays. Several commenters praise the clear and concise code, finding it a valuable learning resource. Some debate the choice of open addressing over separate chaining for the hash table, with proponents of open addressing citing better cache locality and less memory overhead. Others highlight the importance of proper hash functions and the potential performance degradation with high load factors in open addressing. A few users suggest alternative approaches, such as using C++ containers or optimizing for specific use cases, while acknowledging the educational value of Wellons' straightforward C examples. The discussion also touches on the trade-offs of manual memory management and the challenges of achieving both simplicity and performance.
Summary of Comments ( 6 )
https://news.ycombinator.com/item?id=43388296
Hacker News commenters discuss the surprising nature of the discovery, given the problem's long history and apparent simplicity. Some express skepticism about the "disproved" claim, suggesting the Kadane algorithm is a more efficient solution for the original problem than the article implies, and therefore the new hash table isn't a direct refutation. Others question the practicality of the new hash table, citing potential performance bottlenecks and the limited scenarios where it offers a significant advantage. Several commenters highlight the student's ingenuity and the importance of revisiting seemingly solved problems. A few point out the cyclical nature of computer science, with older, sometimes forgotten techniques occasionally finding renewed relevance. There's also discussion about the nature of "proof" in computer science and the role of empirical testing versus formal verification in validating such claims.
The Hacker News comments section for the Wired article "Undergraduate Disproves 40-Year-old Data Science Conjecture, Invents New Kind of Hash Table" contains a lively discussion about the research and its implications.
Several commenters express excitement and praise for the student's achievement, highlighting the significance of disproving a long-standing conjecture as an undergraduate. Some emphasize the rarity and difficulty of such a feat, particularly in theoretical computer science.
A recurring theme in the comments is the discussion around the practicality and performance of the new hash table design in real-world applications. While the theoretical breakthrough is acknowledged, some users question whether the constant factors involved make it competitive with existing hash table implementations. They point out that practical performance often depends on factors not fully captured in theoretical analysis, like cache behavior and memory access patterns. Some also express interest in seeing benchmarks and further research comparing the new design to established methods.
There's debate regarding the precise nature of the student's contribution. Some commenters suggest that "disproving" the conjecture might be too strong a term, as the original conjecture might have been overly broad or misinterpreted. Others delve into the nuances of the conjecture and its implications, discussing the difference between worst-case and average-case performance.
Several commenters discuss the role of the student's advisor and the collaborative nature of research. Some praise the advisor for guiding the student and recognizing the potential of the research, while others suggest that the article might overemphasize the student's independent contribution.
A few commenters express skepticism about the Wired article's presentation, suggesting that the title and some of the language used might be slightly hyperbolic or sensationalized for a general audience. They call for a more nuanced and technical explanation of the research.
Finally, some commenters provide additional context and resources, linking to related research papers and discussions, offering deeper insights into the technical aspects of the work. They also speculate on the potential future applications of the new hash table design, suggesting areas where it might be particularly beneficial.