Abstract
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, therefore, has approximation ratio at most 9 in complete graphs. Furthermore, we construct a family of instances that shows that SGA cannot be better than a 3-approximation algorithm. Our upper and lower bounds hold also for the bounded-length greedy algorithm, a simple on-line algorithm for MEDP.
This work was supported by the Berlin-Zürich Joint Graduate Program “Combinatorics, Geometry, and Computation” (CGC), financed by ETH Zürich and the German Science Foundation (DFG), by the Swiss National Science Foundation under Contract No. 2100-63563.00 (AAPCN), and by EU Thematic Network APPOL II, IST-2001-32007, with funding by the Swiss Federal Office for Education and Science (BBW). A longer version of this paper is available as technical report [1]
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References
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Carmi, P., Erlebach, T., Okamoto, Y. (2003). Greedy Edge-Disjoint Paths in Complete Graphs. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_13
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DOI: https://doi.org/10.1007/978-3-540-39890-5_13
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