SDP Gaps for 2-to-1 and Other Label-Cover Variants

  • Venkatesan Guruswami
  • Subhash Khot
  • Ryan O’Donnell
  • Preyas Popat
  • Madhur Tulsiani
  • Yi Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)

Abstract

In this paper we present semidefinite programming (SDP) gap instances for the following variants of the Label-Cover problem, closely related to the Unique Games Conjecture: (i) 2-to-1 Label-Cover; (ii) 2-to-2 Label-Cover; (iii) α-constraint Label-Cover. All of our gap instances have perfect SDP solutions. For alphabet size K, the integral optimal solutions have value: (i) \(O(1/\sqrt{\log K})\); (ii) O(1/logK); (iii) \(O(1/\sqrt{\log K})\).

Prior to this work, there were no known SDP gap instances for any of these problems with perfect SDP value and integral optimum tending to 0.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Venkatesan Guruswami
    • 1
  • Subhash Khot
    • 2
  • Ryan O’Donnell
    • 1
  • Preyas Popat
    • 2
  • Madhur Tulsiani
    • 3
  • Yi Wu
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon University 
  2. 2.Computer Science DepartmentNew York University 
  3. 3.School of MathematicsInstitute for Advanced Study 

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