• Corpus ID: 6267695

A Lasserre-based $(1+\varepsilon)$-approximation for $Pm \mid p_j=1, \textrm{prec} \mid C_{\max}$

  title={A Lasserre-based \$(1+\varepsilon)\$-approximation for \$Pm \mid p\_j=1, \textrm\{prec\} \mid C\_\{\max\}\$},
  author={Elaine Levey and Thomas Rothvoss},
In a classical problem in scheduling, one has $n$ unit size jobs with a precedence order and the goal is to find a schedule of those jobs on $m$ identical machines as to minimize the makespan. It is one of the remaining four open problems from the book of Garey & Johnson whether or not this problem is $\mathbf{NP}$-hard for $m=3$. We prove that for any fixed $\varepsilon$ and $m$, a Sherali-Adams / Lasserre lift of the time-index LP with a slightly super poly-logarithmic number of $r = (\log(n… 
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