polynomial-time algorithm

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July 1, 2026

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A polynomial-time algorithm is a type of algorithm whose execution time is bounded by a polynomial function of the input size. This means that as the input size (n) grows, the number of steps required by the algorithm increases at a rate that is a power of n, such as n², n³, etc..12

Algorithms that can be solved in polynomial time are considered efficient or "tractable". This is in contrast to algorithms with exponential time complexity, where the execution time grows much more rapidly with the input size, making them "intractable" for large inputs. The P versus NP problem, a major question in computer science, explores whether all problems whose solutions can be quickly verified (NP problems) can also be quickly solved (P problems).321

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linear programming
Leonid Khachiyan discovered a polynomial-time algorithm—in which the number of computational steps grows as a power of the number of variables rather than exponentially—thereby allowing the solution of hitherto inaccessible problems. However, Khachiyan’s algorithm (called the ellipsoid method) was slower than the simplex method when practically applied. In 1984…
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Leonid Khachiyan discovered a polynomial-time algorithm—in which the number of computational steps grows as a power of the number of variables rather than exponentially—thereby allowing the solution of hitherto inaccessible problems. However, Khachiyan’s algorithm (called the ellipsoid method) was slower than the simplex method when practically applied. In 1984…
Read More