# An efficient fully polynomial approximation scheme for the Subset-Sum Problem

@article{Kellerer2003AnEF, title={An efficient fully polynomial approximation scheme for the Subset-Sum Problem}, author={Hans Kellerer and Renata Mansini and Ulrich Pferschy and Maria Grazia Speranza}, journal={J. Comput. Syst. Sci.}, year={2003}, volume={66}, pages={349-370} }

## 74 Citations

A new fully polynomial time approximation scheme for the interval subset sum problem

- Computer Science, MathematicsJ. Glob. Optim.
- 2017

This paper shows that the interval subset sum problem is relatively easy to solve compared to the 0–1 knapsack problem, and identifies several subclasses of the ISSP which are polynomial time solvable (with high probability), albeit the problem is generally NP-hard.

A FPTAS for the Subset Sum Problem with Real Numbers

- Mathematics, Computer Science
- 2021

This paper provides a polynomial algorithm which maximizes the distance to a fixed point over a certain convex set by intersecting the unit hypercube with two relevant half spaces and shows that in case the subset sum problem has a solution, this algorithm gives the correct maximum distance up to an arbitrary chosen precision.

Constant-Time Approximation Algorithms for the Knapsack Problem

- Computer Science, MathematicsTAMC
- 2012

This paper gives a constant-time approximation algorithm for the knapsack problem using weighted sampling, with which it approximates the optimal profit with probability at least 2/3 up to error at most an e -fraction of the total profit.

Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach

- Computer ScienceFAW
- 2008

This work presents an improved enumeration scheme for SSP, and implements it as a complete and exact algorithm (EnumPlus) that solves SSP in expected O(nlogn) time when density, while the previously best density scope is c·n/(logn)2.

An Improved FPTAS for 0-1 Knapsack

- Computer Science
- 2019

An improved algorithm for the 0-1 knapsack problem is presented, with only a (1/ε)1/4 gap from the quadratic conditional lower bound based on (min, +)-convolution, from a multi-level extension of Chan's number-theoretic construction, and a greedy lemma that reduces unnecessary computation spent on cheap items.

An Improved Enumeration Scheme for Subset Sum Problem

- Computer ScienceArXiv
- 2007

This work presents an improved enumeration scheme for SSP, and implements it as a complete and exact algorithm (EnumPlus) that solves SSP in expected O(n log n) time when density d ≥ c · √ n/ log n, while the previously best density scope is d · c · n/(log n) 2.

Approximation Schemes for 0-1 Knapsack

- Computer Science, MathematicsSOSA
- 2018

A simpler algorithm is presented which achieves the same result and is deterministic as the latest polynomial-time approximation scheme, and can actually lead to an improved time bound near O(n + (1/eps)^{12/5}), and still further improvements for small n.

Techniques for solving subset sum problems within a given tolerance

- Computer Science, MathematicsInt. Trans. Oper. Res.
- 2005

Four techniques for solving the subset sum problem are proposed that were found to perform efficiently on large and small problems and can outperform other techniques currently proposed in the literature under certain conditions.

Approximation schemes for non-separable non-linear boolean programming problems under nested knapsack constraints

- Computer ScienceEur. J. Oper. Res.
- 2018

Exact and Approximation Algorithms for Geometric and Capacitated Set Cover Problems

- Mathematics, Computer ScienceAlgorithmica
- 2011

The approximability of the generalization of the antenna problem to include several base stations for antennas is discussed, and in particular its APX-hardness already in the uncapacitated case is shown.

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