আমরা প্রায়শই গণনামূলক জটিলতার ক্ষেত্রে ক্লাসিক গবেষণা এবং প্রকাশনা সম্পর্কে শুনে থাকি (টুরিং, কুক, কার্প, হার্টম্যানিস, রাজবরোভ ইত্যাদি)। আমি ভাবছিলাম যে সেখানে সম্প্রতি প্রকাশিত কাগজগুলি সেমিনাল হিসাবে বিবেচনা করা হয় এবং অবশ্যই পড়তে হবে। সাম্প্রতিককালে আমি গত 5/10 বছর ধরে বলতে চাইছি।
উত্তর:
সাম্প্রতিক কাগজলাসলা বাবাইয়ের দেখায় যে গ্রাফ আইসোমর্ফিিজম কোয়াসি-পি-তে রয়েছে ইতিমধ্যে একটি ক্লাসিক।
এখানে আইসিএম 2018 কার্যক্রমে প্রকাশিত ফলাফলের আরও অ্যাক্সেসযোগ্য এক্সপোজিশন রয়েছে।
গুরুত্ব দর্শকের চোখে। তবে, আমি এটিই বলতে পারি যে ফেডার ard ভার্দি সিএসপি দ্বৈতত্ত্ব অনুমান, এ। বুলাটোভ এবং ডি। ঝুক দ্বারা স্বাধীনভাবে প্রমাণিত হয়েছিল , এটি একটি চূড়ান্ত পরিণতি।
রায়ান উইলিয়ামসের নন-ইউনিফর্ম দুদক সার্কিট লোয়ার সীমানা:
https://people.csail.mit.edu/rrw/acc-lbs.pdf
এবং উর্মিলা মহাদেব দ্বারা কোয়ান্টাম গণনাগুলির শাস্ত্রীয় যাচাইকরণ:
http://ieee-focs.org/FOCS-2018-Papers/pdfs/59f259.pdf
ভাল প্রার্থীদের মত মনে হচ্ছে
This new paper by Hao Huang [1] (not yet peer-reviewed, as far as I know) probably qualifies... it proves the sensitivity conjecture of Nisan and Szegedy, which has been open for ~30 years.
[1] Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture, Hao Huang. Manuscript, 2019. https://arxiv.org/abs/1907.00847
Subhash Khot, Dor Minzer and Muli Safra's 2018 work "Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion" has gotten us "half way" to the Unique Games Conjecture and is methodologically quite interesting according to people more knowledgeable than I. Quoting Boaz Barak,
This establishes for the first time hardness of unique games in the regime for which a sub-exponential time algorithm was known, and hence (necessarily) uses a reduction with some (large) polynomial blowup. While it is theoretically still possible for the unique games conjecture to be false (as I personally believed would be the case until this latest sequence of results) the most likely scenario is now that the UGC is true, and the complexity of the UG(s,c) problem looks something like the following...
The paper has caused some researchers (including Barak) to publicly change their opinion on the truth of the UGC (from false to true).
"On the possibility of faster SAT algorithms" by Pătraşcu & Williams (SODA 2010). It gives tight relations between the complexity of solving CNF-SAT and the complexity of some polynomial problems (k-dominating set, d-sum, etc.).
The results are twofold: either we can improve the complexity of solving some polynomial problems, and thus ETH is false and we get a better algorithm for CNF-SAT. Or ETH is true, and thus we get lower bounds on several polynomial problems.
The paper is surprisingly easy to read and to understand. For me, it's the actual start of fine-grained complexity.
It’s one year beyond the 10-year limit, but “Delegating Computation: Interactive Proofs for Muggles” by Goldwasser, Kalai, and Rothblum has been a hugely influential paper. The main result is that there is an interactive proof for any log-space uniform computation where the prover runs in time poly(n) and the verifier in time n*polylog(n) with polylog(n) bits of communication.
The paper has jump-started research on interactive proofs and verifiable computation for problems in P has been incredibly influential in cryptography where it and the work that followed has had make real-world interactive proofs nearly practical.
For impact, and reach landmark paper by Indyk, and Backurs giving limits to edit distance computation. This paper shows limits to computing, by linking, k-SAT, and SETH. To limit computing the levenshtein distance, between strings, the paper shows tight bounds to computing the edit distance- any better then SETH is violated (SETH may be false in the first place, or even have tighter lower bounds though). The applicability of SETH to possibly problems in P, for getting bounds, or limiting application of algorithms (possibly computation!) is new.
Or this paper by P. Goldberg, and C. Papadimitrou, about a uniform complexity for total functions Towards a unified complexity theory of total functions.
Not sure if this qualifies -- it's both more than 10 years old, and not really a computational complexity result in itself -- but I think the pair of {Graph Structure Theorem, Graph Minor Theorem} is worth noting. It was completed in 2004, and establishes an equivalence between "Bounded topological complexity" and "Does not contain some finite set of minors". Each theorem establishes one direction of the equivalence.
This has primarily had an impact within the realm of parameterized complexity theory, where one of these measures is often bounded, allowing for efficient algorithms that leverage the other. So, I would say that these results have had substantial impact on computational complexity, even if they do not come directly from that field themselves.