https://cs.lozic.me/kinds/conjecture/Recent content in Conjecture on CS TheoremsHugoen-usFri, 16 Jul 2027 12:00:00 +0100https://cs.lozic.me/posts/t037-the-exponential-time-hypothesis-and-fine-grained-complexity/Fri, 16 Jul 2027 12:00:00 +0100https://cs.lozic.me/posts/t037-the-exponential-time-hypothesis-and-fine-grained-complexity/<h2 id="symptom">Symptom</h2> <p>You have a string algorithm. Edit distance between two sequences, the classic dynamic program, $O(n^2)$ time. It has been in production for years.</p> <p>Now the inputs are genome-scale. At $n = 10^5$ characters, $n^2 = 10^{10}$ operations, about <strong>10 seconds</strong> at a billion ops per second. At $n = 10^6$ it is $10^{12}$ operations, about <strong>1000 seconds</strong> — seventeen minutes for one pair of strings. You need to do a million pairs.</p>