Multicriteria Global Minimum Cuts

  title={Multicriteria Global Minimum Cuts},
  author={Amitai Armon and Uri Zwick},
We consider two multicriteria versions of the global minimum cut problem in undirected graphs. In the k-criteria setting, each edge of the input graph has k non-negative costs associated with it. These costs are measured in separate, non-interchangeable, units. In the AND-version of the problem, purchasing an edge requires the payment of all the k costs associated with it. In the OR-version, an edge can be purchased by paying any one of the k costs associated with it. Given k bounds b1,b2… 

Multicriteria cuts and size-constrained k-cuts in hypergraphs

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Unbalanced graph cuts with minimum capacity

  • Peng Zhang
  • Computer Science, Business
    Frontiers of Computer Science
  • 2014
It is proved that the min k-size s-t cut problem is NP-hard, and O(log n)-approximation algorithms for the mink-size S-T cut problem, the min Ek-sizeS-t Cut problem, and the min Eksize cut problem are given.

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A bicriteria approximation algorithm is given for the k-Sparsest Cut problem (to find a k-size cut with the minimum sparsity), which outputs a cut whose sparsity is at most O(logn) times the optimum and whose smaller side has size at least O( logn)k.

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We show that Karger's randomized contraction method (SODA 93) can be adapted to multiobjective global minimum cut problems with a constant number of edge or node budget constraints to give efficient

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On the Parameterized Complexity of Cutting a Few Vertices from a Graph

The parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator is studied and it is shown that if the authors consider edge cuts instead of vertex cuts, the terminal variant of the problem is NP-hard.

A new approximation algorithm for the unbalanced Min s-t Cut problem

  • Peng Zhang
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 2014



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