Approximation Algorithms for Directed Steiner Problems

Moses Charikar, Chandra Chekuri, To Yat Cheung, Zuo Dai, Ashish Goel, Sudipto Guha, Ming Li

Research output: Contribution to journalArticlepeer-review


We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work were the trivial O(k)-approximations. For the directed Steiner tree problem, we design a family of algorithms that achieves an approximation ratio of i(i - 1)k1/i in time O(nik2i) for any fixed i > 1, where k is the number of terminals. Thus, an O(k) approximation ratio can be achieved in polynomial time for any fixed ∈ > 0. Setting i = log k, we obtain an O(log2 k) approximation ratio in quasi-polynomial time. For the directed generalized Steiner network problem we give an algorithm that achieves an approximation ratio of O(k2/3log1/3k), where k is the number of pairs of vertices that are to be connected. Related problems including the group Steiner tree problem, the set TSP problem, and several others in both directed and undirected graphs can be reduced in an approximation preserving fashion to the directed Steiner tree problem. Thus, we obtain the first nontrivial approximations to those as well. All these problems are known to be as hard as the Set cover problem to approximate.

Original languageEnglish (US)
Pages (from-to)73-91
Number of pages19
JournalJournal of Algorithms
Issue number1
StatePublished - Oct 1999
Externally publishedYes


  • Approximation algorithm
  • Directed graph
  • Steiner tree problem

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics


Dive into the research topics of 'Approximation Algorithms for Directed Steiner Problems'. Together they form a unique fingerprint.

Cite this