Edmonds demonstrated that a problem previously thought to require brute force search (a generalization of Perfect Matching) is in fact solvable in polynomial time, illustrating that polynomial time can capture genuinely tractable problems.
A mathematical problem where you try to pair up items (like matching people to jobs) in the best possible way, so that everyone gets exactly one partner and no one is left out.
Tractable problems(as a characteristic of computational difficulty)
Problems that are practically solvable by computers in a reasonable amount of time, rather than problems that would take thousands of years to solve.
polynomial time(Used to characterize feasible computation)
Computational time complexity expressed as t(x)=x^c, where c is a constant and x is the length of the input
In particular, a RAM machine \(A\) consists of a finite sequence of instructions (or program) \(\langle \pi_1,\ldots,\pi_n \rangle\) expressing how numerical operations (typically addition and subtraction) are to be applied to a sequence of registers \(r_1,r_2, \dots\) in which values may be stored and retrieved directly by their index. Showing that one of these models \(\mathfrak{M}_1\) determines the same class of functions as some reference model \(\mathfrak{M}_2\) (such as \(\mathfrak{T}\))