Further Research on Node Based Bottleneck Improvement Problem for Multicut

@inproceedings{Guan2006FurtherRO,
  title={Further Research on Node Based Bottleneck Improvement Problem for Multicut},
  author={Xiucui Guan and Jie Su},
  booktitle={ICIC},
  year={2006}
}
In this paper, we consider the node based bottleneck improvement problem for multicut (NBBIM). The objective is to upgrade a set of nodes with minimum cost such that there is a feasible multicut whose maximum weight is not more than a given value D in the upgraded network. We first show that the problem is $\mathcal{NP}$-hard and MaxSNP-hard for K ≥2 on general directed graphs, where K is the number of source-terminal pairs. Then we present two polynomial algorithms for a special case of… 

References

SHOWING 1-10 OF 47 REFERENCES
Improving multicut in directed trees by upgrading nodes
A class of node based bottleneck improvement problems
Improving Minimum Cost Spanning Trees by Upgrading Nodes
We study budget constrained network upgrading problems. We are given an undirected edge-weighted graph G=(V,E), where node v?V can be upgraded at a cost of c(v). This upgrade reduces the weight of
Approximation Algorithms for Certain Network Improvement Problems
TLDR
A brief overview of the models and definitions of the various problems considered are provided and several new results on the complexity and approximability of network improvement problems are presented.
A Faster Algorithm for Finding the Minimum Cut in a Directed Graph
TLDR
This work considers the problem of finding the minimum capacity cut in a directed network G with n nodes, and shows how to reduce theRunning time of these 2 n − 2 maximum flow algorithms to the running time for solving a single maximum flow problem.
Primal-dual approximation algorithms for integral flow and multicut in trees
TLDR
It is shown that both the maximum integral multicommodity flow and the minimum multicut problem are NP-hard and MAX SNP-hard on trees, although themaximum integral flow can be computed in polynomial time if the edges have unit capacity.
The Capacitated K-Center Problem
The capacitated K-center problem is a basic facility location problem, where we are asked to locate K facilities in a graph and to assign vertices to facilities, so as to minimize the maximum
Multiway cuts in node weighted graphs
A New Formulation and Resolution Method for the p-Center Problem
TLDR
A new integer linear programming formulation for this min-max problem with a polynomial number of variables and constraints is presented, and it is shown that its LP relaxation provides a lower bound tighter than the classical one.
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