Deke Guo
Yunhao Liu
Abstract
In order to improve scalability and to reduce the maintenance overhead for structured peer-to-peer (P2P) networks, researchers have proposed architectures based on several interconnection networks with a fixed-degree and a logarithmical diameter. Among existing fixed-degree interconnection networks, the Kautz digraph has many distinctive topological properties compared to others. It, however, requires that the number of peers have the some given values, determined by peer degree and network diameter. In practice, we cannot guarantee how many peers will join a P2P network at a given time, since a P2P network is typically dynamic with peers frequently entering and leaving. To address such an issue, we propose the balanced Kautz tree and Kautz ring structures. We further design a novel structured P2P system, called BAKE, based on the two structures that has the logarithmical diameter and constant degree, even the number of peers is an arbitrary value. By keeping a total ordering of peers and employing a robust locality-preserved resource placement strategy, resources that are similar in a single or multidimensional attributes space are stored on the same peer or neighboring peers. Through analysis and simulation, we show that BAKE achieves the optimal diameter and as good a connectivity as the Kautz digraph does (almost achieves the Moore bound), and supports the exact as well as the range queries efficiently. Indeed, the structures of balanced Kautz tree and Kautz ring we propose can also be applied to other interconnection networks after minimal modifications, for example, the de Bruijn digraph.
- Banerjee, S. and Sarkar, D. 2001. Hypercube connected rings: A scalable and fault-tolerant logical topology for optical networks. Comput. Commun. 24, 1060--1079. Google Scholar
Digital Library
- Cooper, B. F., Ramakrishnan, R., Srivastava, U., Silberstein, A., Bohannon, P., Jacobsen, H.-A., Puz, N., Weaver, D., and Yerneni, R. 2008. Pnuts: Yahoo!'s hosted data serving platform. Proc. VLDB 1, 2, 1277--1288. Google ScholarDigital Library
- Damerell, R. 1973. On Moore graphs. Proc. Cambridge Phil. Soc. 227--236.Google ScholarCross Ref
- Decandia, G., Hastorun, D., Jampani, M., Kakulapati, G., Lakshman, A., Pilchin, A., Sivasubramanian, S., Vosshall, P., and Vogels, W. 2007. Dynamo: Amazon's highly available key-value store. In Proceedings of the 21st ACM SOSP Conference. ACM, New York, 205--220. Google ScholarDigital Library
- Fiol, M. A. and Llado, A. 1992. The partial line digraph technique in the design of large interconnection networks. IEEE Trans. Comput. 41, 7, 848--857. Google ScholarDigital Library
- Fraigniaud, P. and Gauron, P. 2003. An overview of the content-addressable network D2B. In Proceedings of the 22nd ACM POD Conference. ACM, New York, 151. Google ScholarDigital Library
- Fraigniaud, P. and Gauron, P. 2006. D2B: A De Bruijn based content-addressable network. Theor. Comput. Sci. 355, 1, 65--79. Google ScholarDigital Library
- Gai, A. T. and Viennot, L. 2004. Broose: A practical distributed hashtable based on the De Bruijn topology. In Proceedings of the International Conference on Peer-to-Peer. 167--174. Google ScholarDigital Library
- Guo, D., Liu, Y., and Li, X. 2008. BAKE: A balanced Kautz tree structure for peer-to-peer networks. In Proceedings of the 27th IEEE INFOCOM. IEEE, Los Alamitos, CA.Google Scholar
- Guo, D., Wu, J., Chen, H., and Luo, X. 2007. Moore: An extendable peer-to-peer network based on incomplete Kautz digraph with constant degree. In Proceedings of the 26th IEEE INFOCOM. IEEE, Los Alamitos, CA, 821.Google Scholar
- Guo, D., Wu, J., Liu, Y., Jin, H., Chen, H., and Chen, T. 2011. Quasi-Kautz digraphs for peer-to-peer networks. IEEE Trans. Parallel Distrib. Syst. 22, 6, 1042--1055.Google ScholarDigital Library
- Harvey, N. J. A., Jones, M. B., Saroiu, S., Theimer, M., and Wolman, A. 2003. Skipnet: A scalable overlay network with practical locality properties. In Proceedings of the. 4th USENIX Symposium on Internet Technologies and Systems. Google ScholarDigital Library
- Imase, M. and Itoh, M. 1981. Design to minimize diameter on building-block network. IEEE Trans. Computers 30, 6, 439--442. Google ScholarDigital Library
- Imase, M. and Itoh, M. 1983. A design for directed graphs with minimize diameter. IEEE Trans. Computers 32, 8, 782--784. Google ScholarDigital Library
- Kaashoek, F. and Karger, D. 2003. Koorde: A simple degreeoptimal distributed hash table. In Proceedings of the International Peer-to-Peer Symposium. 98--107.Google Scholar
- Koponen, T., Casado, M., Gude, N., Stribling, J., Poutievski, L., Zhu, M., Ramanathan, R., Iwata, Y., Inoue, H., Hama, T., and Shenker, S. 2010. Onix: A distributed control platform for large-scale production networks. In Proceedings of the 9th USENIX OSDI. 351--364. Google ScholarDigital Library
- Lakshman, A. and Malik, P. 2010. Cassandra: A decentralized structured storage system. Oper. Syst. Rev. 44, 2, 35--40. Google ScholarDigital Library
- Li, D., Lu, X., and Wu, J. 2005. Fissione: A scalable constant degree and low congestion dht scheme based on Kautz graphs. In Proceedings of the IEEE INFOCOM, IEEE, Los Alamitos, CA, 1677--1688.Google Scholar
- Loguinov, D., Casas, J., and Wang, X. 2005. Graph-theoretic analysis of structured peer-to-peer systems: Routing distances and fault resilience. IEEE/ACM Trans. Networks 13, 5, 1107--1120. Google ScholarDigital Library
- Malkhi, D., Naor, M., and Ratajczak, D. 2002. Viceroy: A scalable and dynamic emulation of the butterfly. In Proceedings of the 21st ACM PODC. ACM, New York, 183--192. Google ScholarDigital Library
- Maymounkov, P. and Mazieres, D. 2002. Kademlia: A peer-to-peer information system based on the XOR metric. In Proceedings of the International Peer-to-Peer Symposium. 53--65. Google ScholarDigital Library
- Miller, M. and Siran, J. 2005. Moore graphs and beyond: A survey of the degree/diameter problem. Electron. J. Combinatorics 61, 1--63.Google ScholarCross Ref
- Naor, M. and Wieder, U. 2003. Novel architecture for P2P applications: The continuous-discrete approach. In Proceedings of the ACM Symposium on Parallel Algorithms and Architectures. ACM, New York, 50--59. Google ScholarDigital Library
- Panchapakesan, G. and Sengupta, A. 1999. On a lightwave networks topology using Kautz digraphs. IEEE Computer 48, 10, 1131--1138. Google ScholarDigital Library
- Ratnasamy, S., Francis, P., Handley, M., Karp, R., and Shenker, S. 2001a. A scalable content addressable network. In Proceedings of the ACM SIGCOMM. ACM, New York, 161--172. Google ScholarDigital Library
- Ratnasamy, S., Francis, P., Handley, M., Karp, R. M., and Shenker, S. 2001b. A scalable content-addressable network. In Proceedings of the ACM SIGCOMM. ACM, New York, 161--172. Google ScholarDigital Library
- Rowstron, A. and Druschel, P. 2001. Pastry: Scalable, decentralized object location, and routing for large-scale peer-to-peer systems. Lecture Notes in Computer Science, Vol. 2218, Springer, Berlin, 329--350. Google ScholarDigital Library
- Schlosser, M. T., Sintek, M., Decker, S., and Nejdl, W. 2002. Hypercup - hypercubes, ontologies, and efficient search on peer-to-peer networks. In Proceedings of the 1th International Workshop on Agents and Peer-to-Peer Computing. 112--124. Google ScholarDigital Library
- Shen, H., Xu, C., and Chen, G. 2004. Cycloid: A constant-degree and lookup-efficient P2P overlay network. In Proceedings of. the 18th International Parallel and Distributed Processing Symposium.Google Scholar
- Sivarajan, K. N. and Ramaswami, R. 1994. Lightwave networks based on De Bruijn graphs. IEEE/ACM Trans. Netw. 2, 1, 70--79. Google ScholarDigital Library
- Stoica, I., Morris, R., Karger, D. R., Kaashoek, M. F., and Balakrishnan, H. 2003. Chord: A scalable peer-to-peer lookup service for internet applications. IEEE/ACM Trans. Netw. 11, 1, 17--32. Google ScholarDigital Library
- Tvrdik, P. 1994. Partial Kautz line digraphs with maximal connectivity. Tech. rep. 94-15, LIP ENSL, Lyon, France.Google Scholar
- Xu J. 2001. Topological Structure and Analysis of Interconnection Networks. Kluwer, Amsterdam. Google ScholarDigital Library
- Xu, J., Kumar, A., and Yu, X. X. 2004. On the fundamental tradeoffs between routing table size and network diameter in peer-to-peer networks. IEEE J. Sel. Areas Comm. 22, 1, 151--163. Google ScholarDigital Library
- Zhao, B. Y., Kubiatowicz, J., and Joseph, A. D. 2002. Tapestry: A fault-tolerant wide-area application infrastructure. Comput. Comm. Rev. 32, 1, 81. Google ScholarDigital Library
Index Terms
- Theory and network applications of balanced kautz tree structures
Recommendations
Semantic indexing in structured peer-to-peer networks
The past few years have seen tremendous advances in distributed storage infrastructure. Unstructured and structured overlay networks have been successfully used in a variety of applications, ranging from file-sharing to scientific data repositories. ...
Resilience of structured P2P systems under churn: The reachable component method
Users in a peer-to-peer (P2P) system join and leave the network in a continuous manner. Understanding the resilience properties of P2P systems under high rate of node churn becomes important. In this work, we first find that a lifetime-based dynamic ...
De Bruijn and Kautz digraphs of a rooted tree
In this paper we define the De Bruijn digraphs B(D,m) and the Kautz digraphs K(D,m) of a digraph D in such a way that we recover the original definitions when the digraph D is a path. We establish some general properties of the De Bruijn digraph and the ...
Comments