Proceedings Article10.1109/SFCS.2001.959906
Approximating Directed Multicuts
Joseph Cheriyan,Howard Karloff,Yuval Rabani +2 more
- 14 Oct 2001
- pp 320-328
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TL;DR: The problem of finding a minimum multicut in a directed multicommodity flow network is considered, and the first nontrivial upper bounds on the maxflow-to-min multicut ratio are given.
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Abstract: The seminal paper of Leighton and Rao (1988) and subsequent papers presented approximate min-max theorems relating multicommodity flow values and cut capacities in undirected networks, developed the divide-and-conquer method for designing approximation algorithms, and generated novel tools for utilizing linear programming relaxations. Yet, despite persistent research efforts, these achievements could not be extended to directed networks,excluding a few cases that are "symmetric" and therefore similar to undirected networks. This paper is an attempt to remedy the situation. We consider the problem of finding a minimum multicut in a directed multicommodity flow network, and give the first nontrivial upper bounds on the max flow-to-min multicut ratio. Our results are algorithmic, demonstrating nontrivial approximation guarantees.
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Citations
On the capacity of information networks
TL;DR: An outer bound on the rate region of noise-free information networks is given and it is shown that multicommodity flow solutions achieve the capacity in an infinite class of undirected graphs, thereby making progress on a conjecture of Li and Li.
Minimal multicut and maximal integer multiflow: A survey
TL;DR: The dual relationship between both problems, the maximum integral multiflow and minimum multicut problems and their subproblems, are recalled and complexity results and algorithms are given, firstly in unrestricted graphs and secondly in several special graphs: trees, bipartite or planar graphs.
125
Improved results for directed multicut
Anupam Gupta
- 12 Jan 2003
TL;DR: A simple algorithm is given for the Minimum Directed Multicut problem, and it is shown that it gives an O(√n)-approximation, which improves on the previous approximation guarantee of Cheriyan, Karloff and Rabani.
69
A graph theory approach for designing conservation reserve networks with minimal fragmentation
Hayri Önal,Yicheng Wang +1 more
TL;DR: This article presents a linear integer programming formulation of the habitat fragmentation problem using graph theory concepts and an empirical application of the model to a real data set involving 744 sites and 32 endangered-threatened bird species is presented.
55
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