Title :
Hardness of Coloring 2-Colorable 12-Uniform Hypergraphs with exp(log^{Omega(1)} n) Colors
Author :
Khot, Subhash ; Saket, Rishi
Author_Institution :
New York Univ., New York, NY, USA
Abstract :
We show that it is quasi-NP-hard to color 2-colorable 12-uniform hypergraphs with 2(log n) O(1) colors where n is the number of vertices. Previously, Guruswami et al. [1] showed that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 22 O(vlog log n) colors. Their result is obtained by composing a standard Outer PCP with an Inner PCP based on the Short Code of super-constant degree. Our result is instead obtained by composing a new Outer PCP with an Inner PCP based on the Short Code of degree two.
Keywords :
computational complexity; graph colouring; 2-colorable 12-uniform hypergraph coloring; 2(logn)Ω(1) colors; degree-two short code; graph vertices; inner PCP; quasiNP-hard problem; standard outer PCP; super-constant degree; Color; Complexity theory; Error correction; Error correction codes; Polynomials; Symmetric matrices; Coloring; Hypergraph; Inapproximability; PCP;
Conference_Titel :
Foundations of Computer Science (FOCS), 2014 IEEE 55th Annual Symposium on
Conference_Location :
Philadelphia, PA
DOI :
10.1109/FOCS.2014.30
