We consider the problem of determining constructions with an asymptotically optimal oblivious diameter in small world graphs under the Kleinberg's model. In particular, we give the first general lower bound holding for any monotone distance distribution, that is induced by a monotone generating function. Namely, we prove that the expected oblivious diameter is Ω(log2 n) even on a path of n nodes. We then focus on deterministic constructions and after showing that the problem of minimizing the oblivious diameter is generally intractable, we give asymptotically optimal solutions, that is with a logarithmic oblivious diameter, for paths, trees and Cartesian products of graphs, including d-dimensional grids for any fixed value of d. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Flammini, M., Moscardelli, L., Navarra, A., & Perennes, S. (2005). Asymptotically optimal solutions for small world graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3724 LNCS, pp. 414–428). https://doi.org/10.1007/11561927_30
Mendeley helps you to discover research relevant for your work.