A 4 + ϵ approximation for k-connected subgraphs

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Abstract

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
Volume123
DOIs
StatePublished - Feb 2022

Keywords

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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