| 摘要: |
| Packing 问题构成了一类重要的NP 难问题.对于加权3-Set Packing 问题,把问题转化成加权3-Set Packing
Augmentation 问题进行求解,即主要讨论如何从一个已知的最大加权k-packing 求得一个权值最大的(k+1)-packing.
通过对问题结构的分析,结合Color-Coding 技术,首先给出了一种时间复杂度为O*(10.63k)的参数算法,极大地改进了目前文献中的最好结果O*(12.83k).通过对(k+1)-packing 结构的进一步分析,利用集合划分技术将上述结果降到O*(7.563k). |
| 关键词: 加权3-set packing 加权3-set packing augmentation color-coding |
| DOI： |
| 分类号: |
| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60433020, 60773111 (国家自然科学基金); the
National Basic Research Program of China under Grant No.2008CB17107 (国家重点基础研究发展计划(973)); the Program for New
Century Excellent Talents in University of China under Grant No.NCET-05-0683 (新世纪优秀人才支持计划); the Program for Cheung
Kong Scholars and Innovative Research Team in University of China under Grant No.IRT0661 (长江学者和创新团队发展计划) |
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| Improved Algorithms for Weighted 3-Set Packing |
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FENG Qi-Long,WANG Jian-Xin,CHEN Jian-Er
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| Abstract: |
| Packing problems form an important class of NP-hard problems. In order to solve the weighted 3-set
packing problem, this paper converts the problem to the weighted 3-set packing augmentation problem, and mainly
works on how to construct a maximum weighted (k+1)-packing based on a maximum weighted k-packing. This
paper gives a theoretical study on the structure of the problem and presents a deterministic algorithm of time
O*(10.63k) with color-coding, which significantly improves the previous best result O*(12.83k). After further analyzing the structure of the problem and based on the set dividing method, the above result can be further reduced to O*(7.563k). |
| Key words: weighted 3-set packing weighted 3-set packing augmentation color-coding |
