计算机科学 ›› 2014, Vol. 41 ›› Issue (8): 55-59.doi: 10.11896/j.issn.1002-137X.2014.08.011

• 2013年全国理论计算机科学学术年会 • 上一篇    下一篇

求解二维矩形Packing问题的完备算法

何琨,姚鹏程,李立文   

  1. 华中科技大学计算机科学与技术学院 武汉430074;华中科技大学计算机科学与技术学院 武汉430074;华中科技大学计算机科学与技术学院 武汉430074
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受国家自然科学基金(61173180)资助

Complete Algorithm for 2D Rectangular Packing Problem

HE Kun,YAO Peng-cheng and LI Li-wen   

  • Online:2018-11-14 Published:2018-11-14

摘要: 对于典型的NP难度问题——二维矩形Packing问题,经典完备算法的计算复杂度不仅与待放块的数目相关,也与矩形框的宽和高相关。通过观察二维矩形Packing问题的合法布局的特点,将其与一对有向无环图相对应,并基于Prüfer码进行编码,提出了一种计算复杂度仅与待放块数相关的复杂度较低的完备算法。

关键词: Packing问题,完备算法,计算复杂度,Prüfer编码,有向无环图

Abstract: The classical complete algorithm for the NP hard 2D rectangular packing problem is not only related to the number of items but also related to the width and height of the rectangular container.By observing the characteristics of feasible layouts for this packing problem,we corresponded each feasible layout to a pair of acyclic directed graphs.Then based on the prüfer code,we proposed a new complete algorithm whose computational complexity is only based on the number of items.

Key words: Packing problem,Complete algorithm,Computational complexity,Prüfer code,Directed acyclic graph

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