Document Open Access Logo

On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities

Authors Konstantinos Georgiou, Avner Magen, Iannis Tourlakis



PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2009.2319.pdf
  • Filesize: 127 kB
  • 12 pages

Document Identifiers

Author Details

Konstantinos Georgiou
Avner Magen
Iannis Tourlakis

Cite AsGet BibTex

Konstantinos Georgiou, Avner Magen, and Iannis Tourlakis. On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 203-214, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2319

Abstract

We show that the integrality gap of the standard SDP for \vc~on instances of $n$ vertices remains $2-o(1)$ even after the addition of \emph{all} hypermetric inequalities. Our lower bound requires new insights into the structure of SDP solutions behaving like $\ell_1$ metric spaces when one point is removed. We also show that the addition of all $\ell_1$ inequalities eliminates any solutions that are not convex combination of integral solutions. Consequently, we provide the strongest possible separation between hypermetrics and $\ell_1$ inequalities with respect to the tightening of the standard SDP for \vc.
Keywords
  • Semidefinite Programming
  • Vertex Cover
  • Integrality Gap
  • Hypermetric Inequalities

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail