Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems

  • Authors:

  • Venkatesan Guruswami;Sanjeev Khanna;Rajmohan Rajaraman;Bruce Shepherd;Mihalis Yannakakis

  • Affiliations:

  • MIT Laboratory for Computer Science, 200 Technology Square, Cambridge, MA and Department of Computer Science and Engineering, University of Washington, Box 352350, Seattle, WA;Department of Computer and Information Science, University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA;College of Computer Science, Northeastern University, Boston, MA;Bell Labs, 700 Mountain Avenue, Murray Hill, NJ;Bell Labs, 700 Mountain Avenue, Murray Hill, NJ

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2003

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Abstract

We study the approximability of edge-disjoint paths and related problems. In the edge-disjoint paths (EDP) problem, we are given a network G with source-sink pairs (si, ti), 1 ≤i≤k, and the goal is to find a largest subset of source-sink pairs that can be simultaneously connected in an edge-disjoint manner. We show that in directed networks, for any ε0, EDP is NP-hard to approximate within m1/2-ε. We also design simple approximation algorithms that achieve essentially matching approximation guarantees for some generalizations of EDP. Another related class of routing problems that we study concerns EDP with the additional constraint that the routing paths be of bounded length. We show that, for any ε 0, bounded length EDP is hard to approximate within m1/2-ε even in undirected networks, and give an O(√m)-approximation algorithm for it. For directed networks, we show that even the single source-sink pair case (i.e. find the maximum number of paths of bounded length between a given source-sink pair) is hard to approximate within m1/2-ε, for any ε 0.