Holographic algorithms by Fibonacci gates

ISCAS OpenIR

	Holographic algorithms by Fibonacci gates
	Cai, Jin-Yi (1); Lu, Pinyan (2); Xia, Mingji (3); Cai, J.-Y.(jyc@cs.wisc.edu)
	2013
发表期刊	Linear Algebra and Its Applications
ISSN	243795
卷号	438 期号:2 页码:690-707
摘要	We introduce Fibonacci gates as a polynomial time computable primitive, and develop a theory of holographic algorithms based on these gates. The Fibonacci gates play the role of matchgates in Valiant's theory (Valiant (2008) [19]). They give rise to polynomial time computable counting problems on general graphs, while matchgates mainly work over planar graphs only. We develop a signature theory and characterize all realizable signatures for Fibonacci gates. For bases of arbitrary dimensions we prove a basis collapse theorem. We apply this theory to give new polynomial time algorithms for certain counting problems. We also use this framework to prove that some slight variations of these counting problems are #P-hard. Holographic algorithms with Fibonacci gates prove to be useful as a general tool for classification results of counting problems (dichotomy theorems (Cai et al. (2009) [7])). © 2011 Elsevier Inc. All rights reserved.; We introduce Fibonacci gates as a polynomial time computable primitive, and develop a theory of holographic algorithms based on these gates. The Fibonacci gates play the role of matchgates in Valiant's theory (Valiant (2008) [19]). They give rise to polynomial time computable counting problems on general graphs, while matchgates mainly work over planar graphs only. We develop a signature theory and characterize all realizable signatures for Fibonacci gates. For bases of arbitrary dimensions we prove a basis collapse theorem. We apply this theory to give new polynomial time algorithms for certain counting problems. We also use this framework to prove that some slight variations of these counting problems are #P-hard. Holographic algorithms with Fibonacci gates prove to be useful as a general tool for classification results of counting problems (dichotomy theorems (Cai et al. (2009) [7])). © 2011 Elsevier Inc. All rights reserved.
收录类别	SCI ; EI
关键词	Fibonacci Gates Holographic Algorithm Counting Problems Dichotomy Theorem Signature Theory Matchgates
部门归属	(1) Computer Sciences Department, University of Wisconsin - Madison, 1210 West Dayton Street, Madison, WI 53706, United States; (2) Microsoft Research Asia, #999 Zi Xing Road, Min Hang District, Shanghai, 200241, China; (3) Institute of Software, Chinese Academy of Sciences, #4 South Fourth Street, Zhong Guan Cun, Beijing 100190, China
语种	英语
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16952
专题	中国科学院软件研究所
通讯作者	Cai, J.-Y.(jyc@cs.wisc.edu)
推荐引用方式 GB/T 7714	Cai, Jin-Yi ,Lu, Pinyan ,Xia, Mingji ,et al. Holographic algorithms by Fibonacci gates[J]. Linear Algebra and Its Applications,2013,438(2):690-707.
APA	Cai, Jin-Yi ,Lu, Pinyan ,Xia, Mingji ,&Cai, J.-Y..(2013).Holographic algorithms by Fibonacci gates.Linear Algebra and Its Applications,438(2),690-707.
MLA	Cai, Jin-Yi ,et al."Holographic algorithms by Fibonacci gates".Linear Algebra and Its Applications 438.2(2013):690-707.