Abstract
We consider a variant of the contact process concerning multi-commodity allocation on networks. In this process, the demands for several types of commodities are initially given at some specified vertices and then the demands spread interactively on a contact graph. To allocate supplies in such a dynamic setting, we use a modified version of PageRank vectors, called Kronecker PageRank, to identify vertices for shipping supplies. We analyze both the situation that the demand distribution evolves mostly in clusters around the initial vertices and the case that the demands spread to the whole network. We establish sharp upper bounds for the probability that the demands are satisfied as a function of PageRank vectors.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andersen, R., Chung, F., Lang, K.: Local Partitioning for Directed Graphs Using PageRank. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 166–178. Springer, Heidelberg (2007)
Borgs, C., Chayes, J., Ganesh, A., Saberi, A.: How to distribute antidote to control epidemics. Random Structures & Algorithms 37, 204–222 (2010)
Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems 30, 107–117 (1998)
Chevaleyre, Y., Dunne, P., Endriss, U., Lang, J., Lemaitre, M., Maudet, N., Padget, J., Phelps, S., Rodriguez-Aguilar, J., Sousa, P.: Issues in multiagent resource allocation. Informatica (2006)
Chung, F., Horn, P., Tsiatas, A.: Distributing antidote using PageRank vectors. Internet Mathematics 6, 237–254 (2009)
Dahlquist, G.: Stability and error bounds in the numerical integration of ordinary differential equations. Kungl. Tekn. Högsk. Handl. Stockholm. (130), 87 (1959)
Ganesh, A., Massoulie, L., Towsley, D.: The effect of network topology on the spread of epidemics, vol. 2, pp. 1455–1466. IEEE (2005)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press (1990)
Kiss, I.Z., Green, D.M., Kao, R.R.: Infectious disease control using contact tracing in random and scale-free networks. Journal of the Royal Society, Interface / the Royal Society 3, 55–62 (2006), PMID: 16849217
Merino, C.: The chip-firing game. Discrete Mathematics 302, 188–210 (2005)
Newman, M.: Spread of epidemic disease on networks. Physical Review EÂ 66 (2002)
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
Chung, F., Horn, P., Hughes, J. (2012). Multi-commodity Allocation for Dynamic Demands Using PageRank Vectors. In: Bonato, A., Janssen, J. (eds) Algorithms and Models for the Web Graph. WAW 2012. Lecture Notes in Computer Science, vol 7323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30541-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-30541-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30540-5
Online ISBN: 978-3-642-30541-2
eBook Packages: Computer ScienceComputer Science (R0)