Melissinos, Nikolaos, Pagourtzis, Aris and Triommatis, Theofilos
(2020)
Approximation Schemes for Subset Sum Ratio Problems.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12340 .
pp. 96-107.
|
Text
2003.06622v1.pdf - Published version Download (280kB) | Preview |
Abstract
We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional meaningful requirements. Our main contribution is a generic framework that yields fully polynomial time approximation schemes (FPTAS) for problems in this family that meet certain conditions. We use our framework to design explicit FPTASs for two such problems, namely Two-Set Subset-Sum Ratio and Factor-$r$ Subset-Sum Ratio, with running time $\mathcal{O}(n^4/\varepsilon)$, which coincides with the best known running time for the original $SSR$ problem [15].
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | cs.DS, cs.DS |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 07 Oct 2020 09:00 |
| Last Modified: | 18 Jan 2023 23:29 |
| DOI: | 10.1007/978-3-030-59901-0_9 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3103807 |
Dimensions
Dimensions
