# Multicriteria Global Minimum Cuts

@article{Armon2004MulticriteriaGM, title={Multicriteria Global Minimum Cuts}, author={Amitai Armon and Uri Zwick}, journal={Algorithmica}, year={2004}, volume={46}, pages={15-26} }

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…

## 30 Citations

### Multicriteria cuts and size-constrained k-cuts in hypergraphs

- Computer ScienceMathematical Programming
- 2021

This work shows that min-k-cut in hypergraphs subject to constant lower bounds on part sizes is solvable in polynomial-time for constant k, thus resolving an open problem posed by Guinez and Queyranne (Unpublished manuscript).

### Strongly polynomial bounds for multiobjective and parametric global minimum cuts in graphs and hypergraphs

- Computer Science, MathematicsMath. Program.
- 2015

The multiobjective and parametric versions of the global minimum cut problem in undirected graphs and bounded-rank hypergraphs with multiple edge cost functions are considered and it is shown that the total number of supported non-dominated (SND) cuts is bounded by a polynomial in the numbers of nodes and edges.

### Multicritera Cuts and Size-Constrained k-cuts in Hypergraphs

- Computer Science, MathematicsAPPROX-RANDOM
- 2020

The techniques illustrate the versatility of the random contraction approach to address counting and algorithmic problems concerning multiobjective min-cuts and size-constrained min-$k-cut in hypergraphs and the number of optimal solutions is polynomial.

### Unbalanced graph cuts with minimum capacity

- Computer Science, BusinessFrontiers 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.

### A Strongly Polynomial Time Algorithm for Multicriteria Global Minimum Cuts

- Mathematics, Computer ScienceIPCO
- 2014

It is shown that the number of non-dominated points is O(|V|7) and the first strongly polynomial time algorithm to compute these points is given and this results improve on significantly the super-polynomial bound on the parametric complexity given by Mulmuley.

### Randomized Contractions for Multiobjective Minimum Cuts

- Computer ScienceESA
- 2017

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…

### On the Linear Relaxation of the s-t-cut Problem with Budget Constraints

- MathematicsISCO
- 2020

The linear relaxation of the minimum \(s-t\) cut problem is considered and necessary and sufficient conditions for which it has an integral optimal basic solution are given.

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

- MathematicsMFCS
- 2013

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.

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