| 摘要: |
| 在参数计算与复杂性理论中,一个参数问题是固定参数可解的问题当且仅当该问题是可核心化的.核心化技术是参数化算法设计中应用最为广泛、有效的技术,是参数理论中的一个研究热点.通过实例分析对比了最主要的4种核心化技术的基本思想、应用特点和方法,总结了核心化技术在cover类、packing类和cut类等几个重要领域中的应用成果,展望核心化技术的进一步研究方向并加以分析讨论,针对核心化新技术研究和某些热点问题,提出了可能采取的核心优化方法和思路. |
| 关键词: 核心化 皇冠分解 极值归纳 随机算法 固定参数可解 |
| DOI： |
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| 基金项目:Supported by the National Basic Research Program of China under Grant No.2008CB317107 (国家重点基础研究发展计划(973)); the National Natural Science Foundation of China under Grant Nos.60433020, 60773111 (国家自然科学基金); 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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| Kernelization Techniques and Its Applications to Parameterized Computation |
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LI Shao-Hua,WANG Jian-Xin,CHEN Jian-Er
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| Abstract: |
| According to parameterized complexity theory, a decidable parameterized problem is fixed-parameter tractable if and only if it can be kernelized. Kernelization is the most widely applied and effective technique in the parameterized algorithm design. It is one of the hottest issues in parameterized complexity theory. This paper firstly introduces four main kernelization techniques, which are compared and analyzed with practical examples. Then it discusses how to apply these techniques to parameterized problems, such as covering problems, packing problems and cutting problems. Finally, the paper gives the future research directions about kernelization, especially the new possible kernelization technique and the kernel optimization of several FPT problems. |
| Key words: kernelization crown decomposition extremal induction randomized algorithm fixed-parameter
tractable |
