Linear programming hierarchies suffice for directed steiner tree

Zachary Friggstad, Jochen Könemann, Young Kun-Ko, Anand Louis, Mohammad Shadravan, Madhur Tulsiani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

We demonstrate that ℓ rounds of the Sherali-Adams hierarchy and 2ℓ rounds of the Lovász-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in ℓ-layered graphs from ω (√k) to O(ℓ·logk) where k is the number of terminals. This is an improvement over Rothvoss' result that 2ℓ rounds of the considerably stronger Lasserre SDP hierarchy reduce the integrality gap of a similar formulation to O(ℓ·logk). We also observe that Directed Steiner Tree instances with 3 layers of edges have only an O(logk) integrality gap in the standard LP relaxation, complementing the known fact that the gap can be as large as ω (√k) in graphs with 4 layers.

Original languageEnglish (US)
Title of host publicationInteger Programming and Combinatorial Optimization - 17th International Conference, IPCO 2014, Proceedings
PublisherSpringer Verlag
Pages285-296
Number of pages12
ISBN (Print)9783319075563
DOIs
StatePublished - 2014
Event17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014 - Bonn, Germany
Duration: Jun 23 2014Jun 25 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8494 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014
Country/TerritoryGermany
CityBonn
Period6/23/146/25/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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