TY - GEN

T1 - Efficient rounding for the noncommutative grothendieck inequality

AU - Naor, Assaf

AU - Regev, Oded

AU - Vidick, Thomas

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a noncommutative generalization of the Grothendieck inequality due to Pisier and Haagerup. Our main result, an efficient rounding procedure for this inequality, leads to a constant-factor polynomial time approximation algorithm for an optimization problem which generalizes the Cut Norm problem of Frieze and Kannan, and is shown here to have additional applications to robust principle component analysis and the orthogonal Procrustes problem.

AB - The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a noncommutative generalization of the Grothendieck inequality due to Pisier and Haagerup. Our main result, an efficient rounding procedure for this inequality, leads to a constant-factor polynomial time approximation algorithm for an optimization problem which generalizes the Cut Norm problem of Frieze and Kannan, and is shown here to have additional applications to robust principle component analysis and the orthogonal Procrustes problem.

KW - Grothendieck inequality

KW - Principal component analysis

KW - Rounding algorithm

KW - Semidefinite programming

UR - http://www.scopus.com/inward/record.url?scp=84879833771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879833771&partnerID=8YFLogxK

U2 - 10.1145/2488608.2488618

DO - 10.1145/2488608.2488618

M3 - Conference contribution

AN - SCOPUS:84879833771

SN - 9781450320290

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 71

EP - 80

BT - STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing

T2 - 45th Annual ACM Symposium on Theory of Computing, STOC 2013

Y2 - 1 June 2013 through 4 June 2013

ER -