| holographic algorithms with matchgates capture precisely tractable planar #csp | |
| Cai Jin-Yi; Lu Pinyan; Xia Mingji | |
| 2010 | |
| 会议名称 | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |
| 会议录名称 | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
| 页码 | 427-436 |
| 会议日期 | 40839 |
| 会议地点 | Las Vegas, NV, United states |
| 收录类别 | ei |
| 出版地 | United States |
| ISSN | 2725428 |
| ISBN | 9780770000000 |
| 部门归属 | (1) University of Wisconsin, Madison, WI, United States; (2) Peking University, China; (3) Microsoft Research Asia, United States; (4) Institute of Software, Chinese Academy of Sciences, China |
| 摘要 | Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate computations and holographic algorithms based on them provide a universal methodology to a broad class of counting problems studied in statistical physics community for decades. They capture precisely those problems which are #P-hard on general graphs but computable in polynomial time on planar graphs. More precisely, we prove complexity dichotomy theorems in the framework of counting CSP problems. The local constraint functions take Boolean inputs, and can be arbitrary real-valued symmetric functions. We prove that, every problem in this class belongs to precisely three categories: (1) those which are tractable (i.e., polynomial time computable) on general graphs, or (2) those which are #P-hard on general graphs but tractable on planar graphs, or (3) those which are #P-hard even on planar graphs. The classification criterion is explicit. Moreover, problems in category (2) are tractable on planar graphs precisely by holographic algorithms with matchgates. © 2010 IEEE. |
| 关键词 | Boolean Functions Computer Science Graph Theory Graphic Methods Polynomial Approximation |
| 主办者 | IEEE Comput. Soc. Tech. Comm. Math. Found. Comput. (TCMF); Microsoft Research |
| 语种 | 英语 |
| 内容类型 | 会议论文 |
| URI标识 | http://ir.iscas.ac.cn/handle/311060/8788 |
| 专题 | 2010软件所会议论文 |
| 推荐引用方式 GB/T 7714 | Cai Jin-Yi,Lu Pinyan,Xia Mingji. holographic algorithms with matchgates capture precisely tractable planar #csp[C]. United States,2010:427-436. |
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