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 Omega(log^2 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.

Asymptotically Optimal Solutions for Small World Graphs

FLAMMINI, MICHELE
2008

Abstract

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 Omega(log^2 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.
Small world graph; Social networks; Oblivious diameter
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/2175
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact