Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
6 problems
Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. Their conjectured lower bound is established for…
Anari, Charikar and Ramakrishnan asked whether every fractional perfect matching admits a perfect matching that is α-thin with respect to it, meaning it crosses every cut at most α times the fractional amount. Resolved up to…
Carefully designed stepsize schedules alone accelerate plain gradient descent beyond its textbook O(1/T) rate, without momentum. Whether they can reach the optimal O(T^-2) was open. A lower bound of Omega(T^-1.9319) for last-iterate…
Shellsort's worst-case running time is unknown for the gap sequences actually used in practice. Encoding a permutation as the polynomial σ(1)z + … + σ(n)z^n gives a framework for lower bounds, and yields Ω(N^1.26) for Tokuda's 1992…
How well can an arbitrary boolean constraint satisfaction problem of arity k be approximated in polynomial time? The paper gives a (k/2^k)-approximation, improving the previous best constant of 0.626612 k/2^k due to Makarychev and…
The paper nearly settles the tradeoff between the size of a set system over [n] and its number of full chains, an extremal question raised by Johnson, Leader and Russell as a counterpart to Sperner-type results, and linked by recent work…