
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
41st Annual Symposium on Foundations of Computer Science
Hardness of approximate hypergraph coloring
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
V. Guruswami, J. Hastad, M. Sudan, "Hardness of approximate hypergraph coloring," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 149, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892074, author = {V. Guruswami and J. Hastad and M. Sudan}, title = {Hardness of approximate hypergraph coloring}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {149}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892074}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Hardness of approximate hypergraph coloring SN  02725428 SP EP A1  V. Guruswami, A1  J. Hastad, A1  M. Sudan, PY  2000 KW  computational complexity; minimisation; graph colouring; computational geometry; hardness; approximate hypergraph coloring; covering complexity; probabilistic verifier; minimization problems; PCP verifier; 2colorable 4uniform hypergraph; hardness assumption VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We introduce the notion of covering complexity of a probabilistic verifier. The covering complexity of a verifier on a given input is the minimum number of proofs needed to "satisfy" the verifier on every random string, i.e., on every random string, at least one of the given proofs must be accepted by the verifier. The covering complexity of PCP verifiers offers a promising route to getting stronger inapproximability results for some minimization problems, and in particular (hyper)graph coloring problems. We present a PCP verifier for NP statements that queries only four bits and yet has a covering complexity of one for true statements and a superconstant covering complexity for statements not in the language. Moreover the acceptance predicate of this verifier is a simple NotallEqual check on the four bits it reads. This enables us to prove that for any constant c, it is NPhard to color a 2colorable 4uniform hypergraph using just c colors, and also yields a superconstant inapproximability result under a stronger hardness assumption.
Index Terms:
computational complexity; minimisation; graph colouring; computational geometry; hardness; approximate hypergraph coloring; covering complexity; probabilistic verifier; minimization problems; PCP verifier; 2colorable 4uniform hypergraph; hardness assumption
Citation:
V. Guruswami, J. Hastad, M. Sudan, "Hardness of approximate hypergraph coloring," focs, pp.149, 41st Annual Symposium on Foundations of Computer Science, 2000
Usage of this product signifies your acceptance of the Terms of Use.