Abstract
Social networks are navigable small worlds, in which two arbitrary people are likely connected by a short path of intermediate friends that can be found by a “decentralized” routing algorithm using only local information. We develop a model of social networks based on an arbitrary metric space of points, with population density varying across the points. We consider rank-based friendships, where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is. Our main result is that greedy routing can find a short path (of expected polylogarithmic length) from an arbitrary source to a randomly chosen target, independent of the population densities, as long as the doubling dimension of the metric space of locations is low. We also show that greedy routing finds short paths with good probability in tree-based metrics with varying population distributions.
Part of this work was done while the second author was visiting Yahoo! Research. Thanks to David Barbella, Erik Demaine, George Kachergis, David Karger, Jon Kleinberg, Danny Krizanc, Jasmine Novak, Prabhakar Raghavan, Anna Sallstrom, and Ben Sowell for helpful comments and suggestions.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adamic, L., Adar, E.: How to search a social network. Social Networks 27(3), 187–203 (2005)
Adamic, L., Lukose, R., Huberman, B.: Local search in unstructured networks. In: Handbook of Graphs and Networks. Wiley-VCH, Chichester (2002)
Adamic, L., Lukose, R., Puniyani, A., Huberman, B.: Search in power-law networks. Physical Review Letters E 64(046135) (2001)
Barrière, L., Fraigniaud, P., Kranakis, E., Krizanc, D.: Efficient routing in networks with long range contacts. In: Proc. Intl. Conf. on Distr. Comp. (2001)
Demaine, E., Iacono, J., Langerman, S.: Proximate point searching. Computational Geometry: Theory and Applications 28(1), 29–40 (2004)
Dodds, P., Muhamad, R., Watts, D.: An experimental study of search in global social networks. Science 301, 827–829 (2003)
Duchon, P., Hanusse, N., Lebhar, E., Schabanel, N.: Could any graph be turned into a small world? Theoretical Computer Science 355(1), 96–103 (2006)
Fraigniaud, P.: Greedy routing in tree-decomposed graphs. In: Proc. Eur. Symp. Alg. (2005)
Fraigniaud, P., Gavoille, C., Paul, C.: Eclecticism shrinks even small worlds. In: Proc. Symp. on Princ. of Distr. Comp. (2004)
Iacono, J., Langerman, S.: Proximate planar point location. In: Proc. Symp. on Comp. Geom. (2003)
Karp, B.: Geographic Routing for Wireless Networks. PhD thesis, Harvard (2000)
Karp, B., Kung, H.: GPSR: Greedy perimeter stateless routing for wireless networks. In: Proc. Intl. Conf. on Mobile Computing and Networking (2000)
Kim, B., Yoon, C., Han, S., Jeong, H.: Path finding strategies in scale-free networks. Physical Review Letters E 65(027103) (2002)
Kim, Y., Govindan, R., Karp, B., Shenker, S.: Geographic routing made practical. In: Proc. Symp. on Networked Systems Design and Impl. (2005)
Kleinberg, J.: Navigation in a small world. Nature 406, 845 (2000)
Kleinberg, J.: The small-world phenomenon: An algorithmic perspective. In: Proc. Symp. Theory of Comp. (2000)
Kleinberg, J.: Small-world phenomena and the dynamics of information. In: Advances in Neural Information Processing (2001)
Kleinberg, J.: Complex networks and decentralized search algorithms. In: Proc. International Congress of Mathematicians (2006)
Kumar, R., Liben-Nowell, D., Novak, J., Raghavan, P., Tomkins, A.: Theoretical analysis of geographic routing in social networks. TR MIT-CSAIL-TR-2005-040
Lebhar, E., Schabanel, N.: Close to optimal decentralized routing in long-range contact networks. In: Proc. Intl. Colloq. on Automata, Lang. and Prog. (2004)
Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P., Tomkins, A.: Geographic routing in social networks. Proc. Natl. Acad. Sciences 102(33), 11623–11628 (2005)
Manku, G., Naor, M., Wieder, U.: Know thy neighbor’s neighbor: the power of lookahead in randomized P2P networks. In: Proc. Symp. Theory of Comp. (2004)
Martel, C., Nguyen, V.: Analyzing Kleinberg’s (and other) small-world models. In: Proc. Symp. on Princ. of Distr. Comp. (2004)
Milgram, S.: The small world problem. Psychology Today 1, 61–67 (1967)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge Univ. Press, Cambridge (1995)
Nguyen, V., Martel, C.: Analyzing and characterizing small-world graphs. In: Proc. Symp. on Disc. Alg. (2005)
Şimşek, O., Jensen, D.: A probabilistic framework for decentralized search in networks. In: Proc. Intl. Joint Conf. on AI (2005)
Slivkins, A.: Distance estimation and object location via rings of neighbors. In: Proc. Symp. on Princ. of Distr. Comp. (2005)
Wasserman, S., Faust, K.: Social Network Analysis. Cambridge Univ. Press, Cambridge (1994)
Watts, D., Dodds, P., Newman, M.: Identity and search in social networks. Science 296, 1302–1305 (2002)
Watts, D., Strogatz, S.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kumar, R., Liben-Nowell, D., Tomkins, A. (2006). Navigating Low-Dimensional and Hierarchical Population Networks. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_44
Download citation
DOI: https://doi.org/10.1007/11841036_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38875-3
Online ISBN: 978-3-540-38876-0
eBook Packages: Computer ScienceComputer Science (R0)