A 4 + ϵ approximation for k-connected subgraphs

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We obtain approximation ratio [Formula presented] for the (undirected) k-CONNECTED SUBGRAPH problem, where [Formula presented] is the largest integer such that 2ℓ−1k2ℓ+1≤n. For large values of n this improves the ratio 6 of Cheriyan and Végh [4] when n≥k3 (the case ℓ=1). Our result implies an fpt-approximation ratio 4+ϵ that matches (up to the “+ϵ” term) the best known ratio 4 for k=6,7 for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary symmetric crossing supermodular biset function.

Original languageEnglish
Pages (from-to)64-75
Number of pages12
JournalJournal of Computer and System Sciences
StatePublished - Feb 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.


  • Approximation algorithm
  • Crossing supermodular functions
  • k-connected subgraph


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