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Approximation Algorithms for Orienting Mixed Graphs

  • Michael Elberfeld
  • Danny Segev
  • Colin R. Davidson
  • Dana Silverbush
  • Roded Sharan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6661)

Abstract

Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signaling-regulatory pathways in protein networks. Given a graph and a list of ordered source-target vertex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed source-to-target path. When the input graph is undirected, a sub-logarithmic approximation is known for the problem. However, the approximability of the biologically-relevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithm to this problem. Our algorithm provides a sub-linear guarantee in the general case, and logarithmic guarantees for structured instances.

Keywords

protein-protein interaction network mixed graph graph orientation approximation algorithm 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michael Elberfeld
    • 1
  • Danny Segev
    • 2
  • Colin R. Davidson
    • 3
  • Dana Silverbush
    • 4
  • Roded Sharan
    • 4
  1. 1.Institute of Theoretical Computer ScienceUniversity of LübeckLübeckGermany
  2. 2.Department of StatisticsUniversity of HaifaHaifaIsrael
  3. 3.Faculty of MathematicsUniversity of WaterlooWaterlooCanada
  4. 4.Blavatnik School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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