Multidimensional Cube Packing

We consider the d-dimensional cube packing problem (d-CPP): given a list L of d-dimensional cubes and (an unlimited quantity of) d-dimensional unit-capacity cubes, called bins, find a packing of L into the minimum number of bins. We present two approximation algorithms for d-CPP, for fixed d. The first algorithm has an asymptotic performance bound that can be made arbitrarily close to 2 - (1/2)d . The second algorithm is an improvement of the first and has an asymptotic performance bound that can be made arbitrarily close to 2 - (2/3)d . To our knowledge, these results improve the bounds known so far for d = 2 and d = 3, and are the first results with bounds that are not exponential in the dimension. Key Words: Approximation algorithms, multidimensional bin packing, asymptotic performance.

• Type: Journal
• Year: 2004
• Where: ALGORITHMICA
• Authors: Yoshiharu Kohayakawa, Flávio Keidi Miyazawa, Prabhakar Raghavan, Yoshiko Wakabayashi
• Keywords: ALGORITHMICA 2004, Algorithms, Asymptotic Performance, D-dimensional Cubes