science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most...
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A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems...
35 KB (5,030 words) - 16:53, 9 June 2025
Ulrich; Speranza, Maria Grazia (2003-03-01). "An efficient fully polynomial approximation scheme for the Subset-Sum Problem". Journal of Computer and System...
25 KB (3,750 words) - 18:39, 9 July 2025
Independent set (graph theory) (redirect from Approximation algorithms for the maximum independent set problem)
be approximated to within any approximation ratio c < 1 in polynomial time; similar polynomial-time approximation schemes exist in any family of graphs...
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the tree with cost equal to their distance) there exists a polynomial time approximation scheme devised by Arora (1998). Lozovanu, D.; Zelikovsky, A. (1993)...
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Knapsack problem (redirect from Approximation algorithms for the knapsack problem)
pseudo-polynomial time algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm...
49 KB (7,744 words) - 04:22, 30 June 2025
to: Polynomial-time approximation scheme, an approximation algorithm in computer science Pesetas, Spanish currency PTAS reduction, an approximation-preserving...
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Maximum cut (redirect from Approximation algorithms for the max-cut problem)
no polynomial-time approximation scheme (PTAS), arbitrarily close to the optimal solution, for it, unless P = NP. Thus, every known polynomial-time approximation...
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APX (redirect from Constant-factor approximation algorithm)
problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for...
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(QPTAS) is a variant of a polynomial-time approximation scheme whose running time is quasi-polynomial rather than polynomial. Problems with a QPTAS include...
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Strong NP-completeness (section Strong and weak NP-hardness vs. strong and weak polynomial-time algorithms)
does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition...
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computation when η is extremely small), is known as a Fully Polynomial-Time Approximation Scheme (FPTAS). The dependence on 1/η rather than log(1/η) is a...
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Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems", SIAM Journal...
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close to the optimum (such a family of approximation algorithms is called a polynomial-time approximation scheme or PTAS). Others are impossible to approximate...
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have a constant-factor approximation. In some geometric intersection graphs, there are polynomial-time approximation schemes (PTAS) for finding a MDS...
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does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition...
5 KB (877 words) - 14:57, 21 May 2025
Klaus; Solis-Oba, Roberto (2003). "An asymptotic fully polynomial time approximation scheme for bin covering". Theoretical Computer Science. 306 (1–3):...
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reduction from 3-partition. This means that they have no fully polynomial-time approximation scheme (FPTAS) unless P=NP. Even when m=2, the problems do not have...
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Alan M. Frieze and Ravindran Kannan provided a randomized polynomial time approximation scheme for the problem, providing a sharp contrast between the capabilities...
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Monte Carlo algorithm Numerical analysis Online algorithm Polynomial time approximation scheme Problem size Pseudorandom number generator Quantum algorithm...
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Travelling salesman problem (redirect from Approximation algorithms for the traveling salesman problem)
O{\left(n(\log n)^{O(c{\sqrt {d}})^{d-1}}\right)}} time; this is called a polynomial-time approximation scheme (PTAS). Sanjeev Arora and Joseph S. B. Mitchell...
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cuts must be guillotine cuts (edge-to-edge cuts). Several polynomial-time approximation schemes using sophisticated guillotine cuts. In this setting, the...
19 KB (2,525 words) - 22:49, 2 July 2025
Clique problem (redirect from Approximation algorithms for the clique problem)
compute, it cannot have a fully polynomial-time approximation scheme, unless P = NP. If too accurate an approximation were available, rounding its value...
84 KB (9,905 words) - 16:01, 10 July 2025
the tournaments was proven to have polynomial time approximation schemes (PTAS). One can achieve an approximation ratio of 1/3 (in expectation) by ordering...
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Weak NP-completeness (section Strong and weak NP-hardness vs. strong and weak polynomial-time algorithms)
does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition...
2 KB (429 words) - 23:56, 28 May 2022
the permanent of a matrix with entries from {0,1} has a polynomial-time approximation scheme. In the proof, Jerrum and Sinclair studied the Markov chain...
9 KB (1,428 words) - 07:38, 17 June 2025
Clique cover (section Approximation)
the optimum. Baker's technique can be used to provide a polynomial-time approximation scheme for the problem on planar graphs. The related clique edge...
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proof and also present both a constant factor approximation algorithm and polynomial-time approximation scheme to find the clusters in this setting. Ailon...
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algorithm is a pseudo-polynomial time approximation scheme as well. A ( 3 / 2 + ε ) {\displaystyle (3/2+\varepsilon )} -approximation was given by Jansen...
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parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial time in the...
29 KB (3,440 words) - 18:31, 2 June 2025