A Time-Efficient and Exploratory Algorithm for the Rectangle Packing Problem

Abstract

Today, resource waste is considered as one of the most important challenges in different industries. In this regard, the Rectangle Packing Problem (RPP) can affect noticeably both time and design issues in businesses. In this study, the main objective is to create a set of non-overlapping rectangles so that they have specific dimensions within a rectangular plate with a specified width and an unlimited height. The ensued challenge is an NP-complete problem. NP-complete problem, any of a class of computational problems that still there are no efficient solution for them. Most substantial computer-science problems such as the traveling salesman problem, satisfiability problems (sometimes called propositional satisfiability problem and abbreviated SAT or B-SAT), and graph-covering problems are belong to this class. Essentially, it is complicated to spot the best arrangement with the highest rate of resource utilization by emphasizing the linear computation time. This study introduces a time-efficient and exploratory algorithm for the RPP, including the lowest front-line strategy and a Best-Fit algorithm. The obtained results confirmed that the proposed algorithm can lead to a good performance with simplicity and time efficiency. Our evaluation shows that the proposed model with utilization rate about 94.37% outperforms others with 87.75%, 50.54%, and 87.17% utilization rate, respectively. Consequently, the proposed method is capable to of achieving much better utilization rate in comparison with other mentioned algorithms in just 0.023 s running-time, which is much faster than others.

ACRMiner: An Incremental Approach for Finding Dense and Sparse Rectangular Regions from a 2D Interval Dataset

“…The propsed algorithm was applied on this dataset and the result is shown in Table 4. A total of obtained 10 closed rectangles together with their support counts for the fruit data set.Table4 shows two closed rectangles [31,31,90,90] and [32,32,90,90] with support count of 13, indicating that they are dense regions with density value 13. The dense rectangle [31,31,90,90] shows that if the temperature and humidity values are kept fixed at 31 and 90 respectively then 13 numbers of fruits will be preserved.…”

“…A total of obtained 10 closed rectangles together with their support counts for the fruit data set.Table4 shows two closed rectangles [31,31,90,90] and [32,32,90,90] with support count of 13, indicating that they are dense regions with density value 13. The dense rectangle [31,31,90,90] shows that if the temperature and humidity values are kept fixed at 31 and 90 respectively then 13 numbers of fruits will be preserved. Similarly same number of fruits will be preserved if temperature and humidity values are kept fixed at 32 and 90 respectively.The other solutions such as [30,31,90,95] and [31,32,90,95] allow for some variation in temperature and humidity values and larger rectangles with density values less than 13 may be chosen for this.…”

“…The dense rectangle [31,31,90,90] shows that if the temperature and humidity values are kept fixed at 31 and 90 respectively then 13 numbers of fruits will be preserved. Similarly same number of fruits will be preserved if temperature and humidity values are kept fixed at 32 and 90 respectively.The other solutions such as [30,31,90,95] and [31,32,90,95] allow for some variation in temperature and humidity values and larger rectangles with density values less than 13 may be chosen for this. Numbers of dense closed rectangles computed by the proposed method with varying density thresholds are shown in Table 5.…”

“…Figure 3. Dense Regions R1 and R2for temperature and humidity factors of the fruits as given in Table 1 Various rectangle data mining approaches such as mining maximal empty rectangles [18][19 [20][22] [23], mining holes in large datasets [21] [22] and rectangle packing problems [31] have been proposed for multidimensional data. But all these approaches are not directly based on interval data.…”