Journal Article10.1007/S00493-005-0015-5
Approximating directed multicuts
Joseph Cheriyan,Howard Karloff,Yuval Rabani +2 more
- 08 Oct 2001
- Vol. 25, Iss: 3, pp 251-269
TL;DR: This paper considers the problem of finding a minimum multicut in a directed multicommodity flow network, and gives the first nontrivial upper bounds on the max flow-to-min multicut ratio.
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Abstract: The seminal paper of F.T. Leighton and S. 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. The 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 maxflow-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
Efficient neighborhood search for the Probabilistic Pickup and Delivery Travelling Salesman Problem
TL;DR: An efficient neighborhood search procedure is developed for the probabilistic Pickup and Delivery Travelling Salesman Problem and it is shown that the straightforward approach has an O(n5)complexity.
106
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
Approximating Minimum Multicuts by Evolutionary Multi-objective Algorithms
Frank Neumann,Joachim Reichel +1 more
- 13 Sep 2008
TL;DR: Given a set of k terminal pairs, it is proved that evolutionary algorithms in combination with a multi-objective model of the problem are able to obtain a k-approximation for this problem in expected polynomial time.
References
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L. R. Ford,D. R. Fulkerson +1 more
TL;DR: In this paper, the problem of finding a maximal flow from one given city to another is formulated as follows: "Consider a rail network connecting two cities by way of a number of intermediate cities, where each link has a number assigned to it representing its capacity".
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The geometry of graphs and some of its algorithmic applications
TL;DR: Efficient algorithms for embedding graphs low-dimensionally with a small distortion, and a new deterministic polynomial-time algorithm that finds a (nearly tight) cut meeting this bound.
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The Complexity of Multiterminal Cuts
TL;DR: It is shown that the problem becomes NP-hard as soon as $k=3$, but can be solved in polynomial time for planar graphs for any fixed $k$, if the planar problem is NP- hard, however, if £k$ is not fixed.
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An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms
Tom Leighton,Satish Rao +1 more
- 24 Oct 1988
TL;DR: The main result is an algorithm for performing the task provided that the capacity of each cut exceeds the demand across the cut by a Theta (log n) factor.
Multi-Commodity Network Flows
TL;DR: In this paper, the authors generalize the max-flow min-cut theorem of Ford and Fulkerson to the problem of finding the maximum simultaneous flows of two commodities and give an algorithm similar to the labelling method for constructing the two flows.
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