A 3/2-approximation for big two-bar charts packing

Erzin, Adil; Melidi, Georgii; Nazarenko, Stepan; Plotnikov, Roman

doi:10.1007/s10878-021-00741-1

Cited by 9 publications

(17 citation statements)

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“…The 2-BCPP was first formulated in [11] and then examined in [12,13,14], where the similar problems were described. These problems are the Bin Packing Problem (BPP) [17], the Strip Packing Problem (SPP) [1,8], and the 2-D Vector Packing Problem (2-DVPP) [19].…”

Section: Related Resultsmentioning

confidence: 99%

“…When at least one bar's height of each 2-BC is more than 1/2 (such 2-BCs we called "big"), an O(n 3 )-time 3/2-approximation algorithm was proposed. When each 2-BC is big and additionally non-increasing or non-decreasing, the complexity was reduced to O(n 2.5 ) preserving the ratio [13].…”

Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

“…The paper [14] updates the estimates for the packing length of big 2-BCs, keeping time complexity. In [14], we improve the ratio and give a 5/4-approximation O(n 2.5 )-time algorithm for packing big non-increasing or non-decreasing 2-BCs. For the case of big 2-BCs (not necessarily non-increasing or non-decreasing), we proposed a 16/11-approximation O(n 3 )-time algorithm.…”

Section: Related Resultsmentioning

confidence: 99%

“…New approximation algorithms were proposed in [13] and [14]. Below is a brief description of the algorithms we analyze in this paper, illustrated by an example.…”

Section: Algorithmsmentioning

confidence: 99%

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Approximation Algorithms for Two-Bar Charts Packing Problem

Erzin¹,

Melidi²,

Nazarenko³

et al. 2021

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In the Two-Bar Charts Packing Problem (2-BCPP), it is required to pack the bar charts (BCs) consisting of two bars into the horizontal unit-height strip of minimal length. The bars may move vertically within the strip, but it is forbidden to change the order and separate the chart's bars. Recently, for this new problem, which is a generalization of the Bin Packing Problem (BPP), Strip Packing Problem (SPP), and 2-Dimensional Vector Packing Problem (2-DVPP), several approximation algorithms with guaranteed estimates were proposed. However, after a preliminary analysis of the solutions constructed by approximation algorithms, we discerned that the guaranteed estimates are inaccurate. This fact inspired us to conduct a numerical experiment in which the approximate solutions are compared to each other and with the optimal ones. To construct the optimal solutions or lower bounds for optimum, we use the Boolean Linear Programming (BLP) formulation of 2-BCPP proposed earlier and apply the CPLEX package. We also use a database of instances for BPP with known optimal solutions to construct the instances for the 2-BCPP with known minimal packing length. The results of the simulation make up the main content of this paper.

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Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

“…New approximation algorithms were proposed in [13] and [14]. Below is a brief description of the algorithms we analyze in this paper, illustrated by an example.…”

Section: Algorithmsmentioning

confidence: 99%

See 3 more Smart Citations