The complexity of finding uniform sparsest cuts in various graph classes

P.S. Bonsma, Haitze J. Broersma, Viresh Patel, A.V. Pyatkin

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
44 Downloads (Pure)


Given an undirected graph G=(V,E), the (uniform, unweighted) sparsest cut problem is to find a vertex subset S⊂V minimizing View the MathML source. We show that this problem is NP-complete, and give polynomial time algorithms for various graph classes. In particular, we show that the sparsest cut problem can be solved in linear time for unit interval graphs, and in cubic time for graphs of bounded treewidth. For cactus graphs and outerplanar graphs this can be improved to linear time and quadratic time, respectively. For graphs of clique-width k for which a short decomposition is given, we show that the problem can be solved in time O(n2k+1), where n is the number of vertices in the input graph. We also establish that a running time of the form nO(k) is optimal in this case, assuming that the Exponential Time Hypothesis holds.
Original languageEnglish
Pages (from-to)136-149
Number of pages14
JournalJournal of discrete algorithms
Publication statusPublished - 2012
Externally publishedYes


  • Treewidth
  • Unit interval graph
  • Parameterized complexity
  • Clique-width
  • Sparsest cut


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