Abstract
We study the power of local information algorithms for optimization problems on social and technological networks. We focus on sequential algorithms where the network topology is initially unknown and is revealed only within a local neighborhood of vertices that have been irrevocably added to the output set. This framework models the behavior of an external agent that does not have direct access to the network data, such as a user interacting with an online social network.
We study a range of problems under this model of algorithms with local information. When the underlying graph is a preferential attachment network, we show that one can find the root (i.e. initial node) in a polylogarithmic number of steps, using a local algorithm that repeatedly queries the visible node of maximum degree. This addresses an open question of Bollobás and Riordan. This result is motivated by its implications: we obtain polylogarithmic approximations to problems such as finding the smallest subgraph that connects a subset of nodes, finding the highest-degree nodes, and finding a subgraph that maximizes vertex coverage per subgraph size.
Motivated by problems faced by recruiters in online networks, we also consider network coverage problems on arbitrary graphs. We demonstrate a sharp threshold on the level of visibility required: at a certain visibility level it is possible to design algorithms that nearly match the best approximation possible even with full access to the graph structure, but with any less information it is impossible to achieve a non-trivial approximation. We conclude that a network provider’s decision of how much structure to make visible to its users can have a significant effect on a user’s ability to interact strategically with the network.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alon, N., Rubinfeld, R., Vardi, S., Xie, N.: Space-efficient local computation algorithms. In: SODA, pp. 1132–1139 (2012)
Andersen, R., Chung, F.R.K., Lang, K.J.: Local graph partitioning using pagerank vectors. In: FOCS, pp. 475–486 (2006)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Bollobás, B.: Mathematical results on scale-free random graphs. In: Handbook of Graphs and Networks: From the Genome to the Internet (2003)
Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24(1), 5–34 (2004)
Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.E.: The degree sequence of a scale-free random graph process. Random Struct. Algorithms 18(3), 279–290 (2001)
Brautbar, M., Kearns, M.: Local algorithms for finding interesting individuals in large networks. In: Innovations in Theoretical Computer Science (ITCS), pp. 188–199 (2010)
Doerr, B., Fouz, M., Friedrich, T.: Social networks spread rumors in sublogarithmic time. In: STOC, pp. 21–30 (2011)
Easley, D., Kleinberg, J.: Networks, Crowds, and Markets, reasoning about a Highly Connected World. Cambridge University Press (2010)
Faloutsos, C., McCurley, K.S., Tomkins, A.: Fast discovery of connection subgraphs. In: KDD, pp. 118–127 (2004)
Giakkoupis, G., Sauerwald, T.: Rumor spreading and vertex expansion. In: SODA, pp. 1623–1641 (2012)
Giakkoupis, G., Schabanel, N.: Optimal path search in small worlds: dimension matters. In: STOC, pp. 393–402 (2011)
Goldreich, O.: Introduction to Testing Graph Properties. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 105–141. Springer, Heidelberg (2010)
Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20(4), 374–387 (1998)
Hassidim, A., Kelner, J.A., Nguyen, H.N., Onak, K.: Local graph partitions for approximation and testing. In: FOCS, pp. 22–31 (2009)
Kleinberg, J.M.: The small-world phenomenon: an algorithm perspective. In: STOC, pp. 163–170 (2000)
Naor, M., Stockmeyer, L.: What can be computed locally? In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, STOC 1993, pp. 184–193. ACM, New York (1993)
Rubinfeld, R., Shapira, A.: Sublinear time algorithms. SIAM Journal on Discrete Math. 25, 1562–1588 (2011)
Rubinfeld, R., Tamir, G., Vardi, S., Xie, N.: Fast local computation algorithms. In: ITCS, pp. 223–238 (2011)
Spielman, D.A., Teng, S.-H.: A local clustering algorithm for massive graphs and its application to nearly-linear time graph partitioning. CoRR abs/0809.3232 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borgs, C., Brautbar, M., Chayes, J., Khanna, S., Lucier, B. (2012). The Power of Local Information in Social Networks. In: Goldberg, P.W. (eds) Internet and Network Economics. WINE 2012. Lecture Notes in Computer Science, vol 7695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35311-6_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-35311-6_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35310-9
Online ISBN: 978-3-642-35311-6
eBook Packages: Computer ScienceComputer Science (R0)