
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
2011 26th Annual IEEE Conference on Computational Complexity
Lower Bounds on Query Complexity for Testing BoundedDegree CSPs
San Jose, California USA
June 08June 11
ISBN: 9780769544113
ASCII Text  x  
Yuichi Yoshida, "Lower Bounds on Query Complexity for Testing BoundedDegree CSPs," 2012 IEEE 27th Conference on Computational Complexity, pp. 3444, 2011 26th Annual IEEE Conference on Computational Complexity, 2011.  
BibTex  x  
@article{ 10.1109/CCC.2011.10, author = {Yuichi Yoshida}, title = {Lower Bounds on Query Complexity for Testing BoundedDegree CSPs}, journal ={2012 IEEE 27th Conference on Computational Complexity}, volume = {0}, year = {2011}, issn = {10930159}, pages = {3444}, doi = {http://doi.ieeecomputersociety.org/10.1109/CCC.2011.10}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2012 IEEE 27th Conference on Computational Complexity TI  Lower Bounds on Query Complexity for Testing BoundedDegree CSPs SN  10930159 SP34 EP44 A1  Yuichi Yoshida, PY  2011 KW  Property testing KW  constraint satisfaction problems KW  boundeddegree model KW  lower bound VL  0 JA  2012 IEEE 27th Conference on Computational Complexity ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.10
In this paper, we consider lower bounds on the query complexity for testing CSPs in the boundeddegree model. We mainly consider Boolean CSPs allowing literals. First, for any "symmetric'' predicate P:\bit^{k}\to \bit except \equ where k\geq 3, we show that every (randomized) algorithm that distinguishes satisfiable instances of \csp{$P$} from instances (P^{1}(0)/2^k\epsilon)far from satisfiability requires \Omega(n^{1/2+\delta}) queries where n is the number of variables and \delta>0 is a constant that depends on P and \epsilon. This breaks a natural lower bound \Omega(n^{1/2}), which is obtained by the birthday paradox. We also show that every onesided error tester requires \Omega(n) queries for such P. These results are hereditary in the sense that the same results hold for any predicate Q such that P^{1}(1)\subseteq Q^{1}(1). For \equ, we give a onesided error tester whose query complexity is \tilde{O}(n^{1/2}). Also, for \txor (or, equivalently \textsf{E2LIN2}), we show an \Omega(n^{1/2+\delta}) lower bound for distinguishing instances between \epsilonclose to and (1/2\epsilon)far from satisfiability. Next, for the general \kcsp over the binary domain, we show that every algorithm that distinguishes satisfiable instances from instances (12k/2^k\epsilon)far from satisfiability requires \Omega(n) queries. The matching NPhardness is not known, even assuming the Unique Games Conjecture or the dto1 Conjecture. As a corollary, for \mislong on graphs with n vertices and a degree bound d, we show that every approximation algorithm within a factor d/\poly\log d and an additive error of \epsilon n requires \Omega(n) queries. Previously, only superconstant lower bounds were known.
Index Terms:
Property testing, constraint satisfaction problems, boundeddegree model, lower bound
Citation:
Yuichi Yoshida, "Lower Bounds on Query Complexity for Testing BoundedDegree CSPs," ccc, pp.3444, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
Usage of this product signifies your acceptance of the Terms of Use.