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 ...

These algorithms are significant because they can solve the noncommutative weighted Edmonds' problem in polynomial time, demonstrating that certain complex problems can be tackled efficiently [2].

The amount of time it takes for an algorithm to solve a polynomial function, which is a mathematical expression that does not contain fractions or negative numbers. The time is proportional to the ...

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 ...

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.

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.