Abstract
We consider a scenario of information broadcast where a source node distributes data in parallel over a fixed number of trees spanning over a large audience of nodes. The trees used for data dissemination are called distribution topology. Particular implementations of this scenario are peer-to-peer live streaming systems. Encoding data partially redundant, nodes are satisfied as long as they receive packets in at least a certain portion of trees. Otherwise, they are called isolated.
We study distribution topologies limiting the worst-case consequences of attacks suddenly removing nodes from the trees. In particular, we aim to minimize the maximum possible number of isolated nodes for each number of removed nodes. We show necessary conditions on distribution topologies closely approximating this goal. Then, we demonstrate that the attack-resilience of topologies adhering to these conditions is characterized by specific matrices that have to be Orthogonal Arrays of maximum strength. The computational complexity of finding such matrices for arbitrary dimensions is a long-standing research problem. Our results show that finding representatives of the studied distribution topologies is at least as hard as this problem.
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
Goyal, V.: Multiple description coding: compression meets the network. IEEE Signal Proc. Mag. 18(5), 74–93 (2001)
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland Mathematical Library (1993)
Brinkmeier, M., Schaefer, G., Strufe, T.: Optimally DoS Resistant P2P Topologies for Live Multimedia Streaming. IEEE T. Parall. Distr. 20(6), 831–844 (2009)
Castro, M., Druschel, P., Kermarrec, A.M., Nandi, A., Rowstron, A., Singh, A.: Splitstream: high-bandwidth multicast in cooperative environments. SIGOPS Oper. Syst. Rev. 37, 298–313 (2003)
Padmanabhan, V.N., Wang, H.J., Chou, P.A., Sripanidkulchai, K.: Distributing streaming media content using cooperative networking. In: NOSSDAV 2002, pp. 177–186. ACM, New York (2002)
Grau, S., Fischer, M., Schäfer, G.: On the Dependencies between Source Neighbors in Optimally DoS-stable P2P Streaming Topologies. In: IEEE International Conference on Distributed Computing Systems 2011, ICDCS, pp. 121–130 (2011)
Dán, G., Fodor, V.: Stability and performance of overlay multicast systems employing forward error correction. Perform. Eval. 67, 80–101 (2010)
Hedayat, A.S., Sloane, N.J.A., Stufken, J.: Orthogonal Arrays: Theory and Applications. Springer, New York (1999)
Diestel, R.: Graph Theory, 3rd edn. Graduate Texts in Mathematics, vol. 173. Springer, Heidelberg (2005)
Grau, S.: On the Stability of Distribution Topologies in Peer-to-Peer Live Streaming Systems. PhD thesis, Technische Universität Ilmenau, Germany (2012)
Roth, R.M.: Introduction to Coding Theory. Cambridge University Press (2006)
Segre, B.: Curve razionali normali e k-archi negli spazi finiti. Ann. Math. Pura Appl. (39), 357–359 (1955)
Nguyen, N.K., Liu, M.Q.: An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays. Comput. Stat. Data An. 52, 5269–5276 (2008)
Xu, H.: An Algorithm for Constructing Orthogonal and Nearly Orthogonal Arrays with Mixed Levels and Small Runs. Technometrics 44, 356–368 (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
Grau, S. (2012). Attack-Resilient Multitree Data Distribution Topologies. In: Baldoni, R., Flocchini, P., Binoy, R. (eds) Principles of Distributed Systems. OPODIS 2012. Lecture Notes in Computer Science, vol 7702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35476-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-35476-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35475-5
Online ISBN: 978-3-642-35476-2
eBook Packages: Computer ScienceComputer Science (R0)