At the same time, progress in invariant theory has contributed significantly to the development of deterministic algorithms by establishing concrete polynomial degree bounds for matrix invariants ...

Mark Jerrum, Alistair Sinclair (UC Berkeley) and Eric Vigoda (Georgia Tech) received the Association for Computing Machinery (ACM) Test of Time Award at a virtual ceremony on Wednesday 23 June at the ...

Mathematicians believe that this is unsolvable by polynomial-time algorithms in Turing’s framework. Factoring an integer means finding a smaller integer greater than 1 that can divide the integer.

We prove that the classic policy-iteration method [Howard, R. A. 1960. Dynamic Programming and Markov Processes. MIT, Cambridge] and the original simplex method with the most-negative-reduced-cost ...

We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in a real vector space of dimension two. Previous work shows that optimizing a ...

That is, problems for which efficient algorithms exist are only a subset of the problems for which yes instances can be verified in polynomial time. However, this has not been proved.