@inbook{7266d5766ec8469697e2017848fab3bc,

title = "Greedy edge-disjoint paths in complete graphs",

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.",

keywords = "Approximation algorithm, Greedy algorithm, Shortening lemma",

author = "Paz Carmi and Thomas Erlebach and Yoshio Okamoto",

year = "2003",

month = jan,

day = "1",

doi = "10.1007/978-3-540-39890-5_13",

language = "English",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "143--155",

editor = "Bodlaender, {Hans L.}",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

address = "Germany",

}