Approximating the cut-norm via Grothendieck's inequality

The cut-norm ||A||C of a real matrix A = (aij)iR,jS is the maximum, over all I R, J S of the quantity | iI,jJ aij|. This concept plays a major role in the design of efficient approximation algorithms for dense graph and matrix problems. Here we show that the problem of approximating the cut-norm of a given real matrix is MAX SNP hard, and provide an efficient approximation algorithm. This algorithm finds, for a given matrix A = (aij)iR,jS, two subsets I R and J S, such that | iI,jJ aij| ||A||C, where > 0 is an absolute constant satisfying > 0.56. The algorithm combines semidefinite programming with a novel rounding technique based on Grothendieck's Inequality.

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Noga Alon, Assaf Naor
• Keywords: Algorithms, Efficient Approximation, II, JJ Aij|, STOC 2004