Complexity Theory and Polynomial Time Algorithms Publication Trend The graph below shows the total number of publications each year in Complexity Theory and Polynomial Time Algorithms.

Mathematicians have long sought to develop algorithms that can compare any two graphs. In practice, many ...

These “ polynomial-time algorithms ” are efficient algorithms, meaning it’s practical to use computers to solve instances of them. Thousands of other solvable problems are not known to have polynomial ...

A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries Mark Jerrum, Alistair Sinclair (UC Berkeley) and Eric Vigoda (Georgia Tech) received the Association ...

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 ...

In “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” Shor showed how, using a hypothetical quantum computer, you could efficiently solve ...

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.

These “ polynomial-time algorithms ” are efficient algorithms, meaning it’s practical to use computers to solve instances of them.

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.