• Corpus ID: 15379542

Directed Steiner Tree and the Lasserre Hierarchy

  title={Directed Steiner Tree and the Lasserre Hierarchy},
  author={Thomas Rothvoss},
  • T. Rothvoss
  • Published 23 November 2011
  • Computer Science, Mathematics
  • ArXiv
The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic graphs where the nodes are arranged in L <= log |X| levels. Unfortunately the natural LP formulation has a |X|^(1/2) integrality gap already for 5 levels. We show that for every L, the O(L)-round Lasserre Strengthening of this LP has integrality gap O(L log |X… 

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