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2004
ACM

Approximating the cut-norm via Grothendieck's inequality

14 years 3 months ago
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.
Noga Alon, Assaf Naor
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2004
Where STOC
Authors Noga Alon, Assaf Naor
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