Special Circle Packing problem, what is the least number of circles that can be fitted inside another circle? Background & Motivation: It is a brand new problem I came up with while studying Apollonian gaskets and circle packing, which requires more brain power than I have.

2020年8月27日 · I'm studying Bin Packing Problem for my thesis and I meet this definition of the decision verson of the problem in the book "Computers and Intractability" by Michael R. Garey and David S.

2024年9月23日 · I have gotten interested in square packing problems recently and I came across a problem called the Mrs. Perkins' Quilt Problem. But I have had some trouble understanding it. To state the conditions of the problem strictly, we can write this (taken from an online article): The dissection of a square of side into a number of smaller squares.

2024年10月6日 · It is a brand new problem I came up with while studying Apollonian gaskets and circle packing, which requires more brain power than I have. It is currently at the beginning stage of study. I hope this problem gets noticed by more mathematicians and I hope for a solution.

Number of Permutations in a Bin Packing Problem. 0. Goldilocks Packing type problem. 2.

2018年2月11日 · I now think that the smallest d which allows a million squares to be packed is probably 22,515,570 (=$2×3^{4}×5×7×11×19^{2}$). This d-value first fails on packing the square with side 1/1,000,784. If there is a smaller d which allows the million-square packing, then that d is less than 22 million.

2015年5月10日 · First of all, could someone please let me know if there is any classic name for this problem. I am not sure what to call this problem. It would be great if someone could help me to solve this. Note 1: The items in the bags are not identical and therefore we cannot combine different items in the same bag.

2022年10月12日 · The bin pack problem denotes the process of assigning a set of n items into a minimal number of bins of capacity c. It can be simply formulated as an ILP as per the below description: My question is : how to express an additional constraint in the ILP formulation such that the load on the used bins is as much as possible balanced or fair across ...

2017年10月31日 · I know that, e.g., for fixed number of bins there is a pseudo-polynomial time algorithm ( Bin packing with fixed number of bins revisited, Klaus Jansen et al.), but I don't see how it translates the the fixed bin size.

2016年8月15日 · In general, the problem of packing rectangles optimally is known to be NP-hard. If you want to obtain other packing of these rectangles or packing other rectangles but only need an near optimal solution, there are commercial software which does the job.