A $4/3\cdot OPT+2/3$ approximation for big two-bar charts packing problem
Optimization and Control
2022-12-05 v1 Discrete Mathematics
Abstract
Two-Bar Charts Packing Problem is to pack two-bar charts (2-BCs) in a minimal number of unit-capacity bins. This problem generalizes the strongly NP-hard Bin Packing Problem. We prove that the problem remains strongly NP-hard even if each 2-BC has at least one bar higher than 1/2. Next we consider the case when the first (or second) bar of each 2-BC is higher than 1/2 and show that the -time greedy algorithm with preliminary lexicographic ordering of 2-BCs constructs a packing of length at most , where is optimum. Eventually, this result allowed us to present an -time algorithm that constructs a packing of length at most for the NP-hard case when each 2-BC has at least one bar higher than 1/2.
Cite
@article{arxiv.2212.00944,
title = {A $4/3\cdot OPT+2/3$ approximation for big two-bar charts packing problem},
author = {Adil Erzin and Alexander Kononov and Georgii Melidi and Stepan Nazarenko},
journal= {arXiv preprint arXiv:2212.00944},
year = {2022}
}