Approximating multiroot 3-outconnected subgraphs

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Consider the following problem: Given an undirected graph with nonnegative edge costs and requirements ku for every node u, find a minimum-cost subgraph that contains max{ku, kv} internally disjoint paths between every pair of nodes u, v. For k = max ku ≥ 2, this problem is NP-hard. The best-known algorithm for it has an approximation ratio of 2(k - 1). For a general instance of the problem, for no value of k ≥ 2, a better approximation algorithm was known. We consider the case of small requirements ku ∈ {1, 2, 3}; these may arise in applications, as, in practical networks, the connectivity requirements are usually rather small. For this case, we give an algorithm with an approximation ratio of 10/3. This improves the best previously known approximation ratio of 4. Our algorithm also implies an improvement for arbitrary k. In the case in which we have an initial graph which is 2-connected, our algorithm achieves an approximation ratio of 2.

Original languageEnglish
Pages (from-to)172-179
Number of pages8
Issue number3
StatePublished - Oct 2000


  • Approximation algorithm
  • Rooted 3-outconnected subgraph


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