The Maximum Edge-Disjoint Paths Problem in Bidirected Trees

  • Authors:
  • Thomas Erlebach;Klaus Jansen

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2001

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Abstract

A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edge-disjoint paths problem is to select a maximum-cardinality subset of the paths such that the selected paths are edge-disjoint. This problem can be solved optimally in polynomial time for bidirected trees of constant degree but is APX-hard for bidirected trees of arbitrary degree. For every fixed $\varepsilon 0$, a polynomial-time $(5/3+\varepsilon)$-approximation algorithm is presented.