holographic algorithms with matchgates capture precisely tractable planar #csp
文献类型：会议论文
| 作者 | Cai Jin-Yi ; Lu Pinyan ; Xia Mingji |
| 出版日期 | 2010 |
| 会议名称 | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |
| 会议日期 | 40839 |
| 会议地点 | Las Vegas, NV, United states |
| 关键词 | Boolean functions Computer science Graph theory Graphic methods Polynomial approximation |
| 页码 | 427-436 |
| 英文摘要 | 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. |
| 收录类别 | EI |
| 会议主办者 | IEEE Comput. Soc. Tech. Comm. Math. Found. Comput. (TCMF); Microsoft Research |
| 会议录 | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
 |
| 会议录出版地 | United States |
| 语种 | 英语 |
| ISSN号 | 2725428 |
| ISBN号 | 9780770000000 |
| 源URL | [http://124.16.136.157/handle/311060/8788]  |
| 专题 | 软件研究所_软件所图书馆_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]. 见:2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010. Las Vegas, NV, United states. 40839. |
入库方式： OAI收割
来源：软件研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。