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Bonsma, P.S. and Broersma, H.J. and Patel, V. and Pyatkin, A.
(2011)
The complexity status of problems related to sparsest cuts.
In: Proceedings of the 21st International Workshop on Combinatorial Algorithms, IWOCA 2010, 26-28 July 2010, London, UK.
pp. 125-135.
Lecture Notes in Computer Science 6460.
Springer Verlag.
ISSN 0302-9743
ISBN 978-3-642-19221-0
Full text available as:
Official URL: http://dx.doi.org/10.1007/978-3-642-19222-7_14 AbstractGiven an undirected graph G = (V,E) with a capacity function w on the edges, the sparsest cut problem is to find a vertex subset S ⊂ V minimizing ∑ e ∈ E(S,V ∖ S) w(e)/(|S||V ∖ S|). This problem is NP-hard. The proof can be found in [16]. In the case of unit capacities (i. e. if w(e) = 1 for every e ∈ E) the problem is to minimize |E(S,V ∖ S)|/(|S||V ∖ S|) over all subsets S ⊂ V. While this variant of the sparsest cut problem is often assumed to be NP-hard, this note contains the first proof of this fact. We also prove that the problem is polynomially solvable for graphs of bounded treewidth.
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