# Greedy Edge-Disjoint Paths in Complete Graphs

@inproceedings{Carmi2003GreedyEP, title={Greedy Edge-Disjoint Paths in Complete Graphs}, author={Paz Carmi and Thomas Wilhelm Erlebach and Yoshio Okamoto}, booktitle={WG}, year={2003} }

The maximum edge-disjoint paths problem (MEDP) is one of the most classical NP-hard problems. We study the approximation ratio of a simple and practical approximation algorithm, the shortest-path-first greedy algorithm (SGA), for MEDP in complete graphs. Previously, it was known that this ratio is at most 54. Adapting results by Kolman and Scheideler [Proceedings of SODA, 2002, pp. 184–193], we show that SGA achieves approximation ratio 8F+1 for MEDP in undirected graphs with flow number F and…

## 15 Citations

### The maximum edge-disjoint paths problem in complete graphs

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2008

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It is shown that no on-line algorithm for the considered problem is ever better than a 1.50-approximation, and the proposed approximation techniques are adapted for other routing problems in complete graphs, leading to an off-line 3- approximation (on-line 4-Approximation) for routing with minimum edge load.

### Path problems in generalized stars, complete graphs, and brick wall graphs

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A more sophisticated ACO algorithm is evolved based on the (basic) approach in Blesa and Blum (2004) and the quality of the solutions they obtain are susceptible to improvement.

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It is shown that, for a fixed number of source-sink pairs, the minimum multicut problem is polynomial-time solvable in planar graphs and in bounded tree-width graphs.

### Analyzing approximation algorithms with the dual-fitting method 1 A greedy algorithm for S ET C OVER

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One of the best examples of combinatorial approximation algorithms is a greedy algorithm approximating the (weighted) SET COVER problem, where the goal is to find a sub-family of S with minimum total weight such that the union of the sub- family is U.

### On Solving the Maximum Disjoint Paths Problem with Ant Colony Optimization

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The efficient use of modern communication networks depends on our capabilities for solving a number of demanding algorithmic problems, some of which are concerned with the allocation of network…

### A bibliography on multicut and integer multiflow problems

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- 2004

We present a bibliography about the maximum integral multiflow and the minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. Some…

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A polynomial-time algorithm that solves the problem optimally provided that the calls are given as pre-specified paths in the ring and can be derandomized by means of Hadamard matrices keeping the same approximation ratio.

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