Skip to main content
SpringerLink
Log in

A fault tolerant peer-to-peer spatial data structure

  • Published:
Peer-to-Peer Networking and Applications Aims and scope Submit manuscript

Abstract

In recent years, many layered indexing techniques over distributed hash table (DHT)-based peer-to-peer (P2P) systems have been proposed to realize distributed range search. In this paper, we present a fault tolerant constant degree dynamic Distributed Spatial Data Structure called DSDS that supports orthogonal range search on a set of N d-dimensional points published on n nodes. We describe a total order binary relation algorithm to publish points among supernodes and determine supernode keys. A non-redundant rainbow skip graph is used to coordinate message passing among nodes. The worst case orthogonal range search cost in a d-dimensional DSDS with n nodes is \(O\left (\log n+m+\frac {K}{B}\right )\) messages, where m is the number of nodes intersecting the query, K is the number of points reported in range, and B is the number of points that can fit in one message. A complete backup copy of data points stored in other nodes provides redundancy for our DSDS. This redundancy permits answering a range search query in the case of failure of a single node. For single node failure, the DSDS routing system can be recovered to a fully functional state at a cost of O(log n) messages. Backup sets in DSDS nodes are used to first process a query in the most efficient dimension, and then used to process a query containing the data in a failed node in d-dimensional space. The DSDS search algorithm can process queries in d-dimensional space and still tolerate failure of one node. Search cost in the worst case with a failed node increases to \(O\left (d\log n+dm+\frac {K}{B}\right )\) messages for d dimensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Andrzejak A, Xu Z (2002) Scalable, efficient range queries for grid information services. In: Proceedings. Second international conference on Peer-to-peer computing, 2002.(p2p 2002). IEEE, pp 33–40

  2. Aspnes J, Shah G (2007) Skip graphs. ACM Trans Algorithm (TALG) 3(4):37

    Article  MathSciNet  MATH  Google Scholar 

  3. Bharambe AR, Agrawal M, Seshan S (2004) Mercury: supporting scalable multi-attribute range queries. ACM SIGCOMM Comput Commun Rev 34(4):353–366

    Article  Google Scholar 

  4. Birkhoff G (1967) Lattice theory, vol. 25 American Mathematical Society

  5. Bisadi P, Nickerson BG (2011) Orthogonal range search using a distributed computing model. In: Proceedings of 23rd canadian conference on computational geometry (CCCG 2011), pp 337–342

  6. Crainiceanu A, Linga P, Gehrke J, Shanmugasundaram J (2004) P-tree: a p2p index for resource discovery applications. In: Proceedings of the 13th international world wide web conference on alternate track papers & posters. ACM, pp 390–391

  7. Goodrich MT, Nelson MJ, Sun JZ (2006) The rainbow skip graph: a fault-tolerant constant-degree distributed data structure. In: Proceedings of the seventeenth annual ACM-SIAM symposium on discrete algorithm. ACM, pp 384–393

  8. Goodrich MT, Nelson MJ, Sun JZ (2009) The rainbow skip graph: A fault-tolerant constant-degree p2p relay structure. arXiv preprint arXiv:0905.2214

  9. Gupta A, Agrawal D, El Abbadi A (2003) Approximate range selection queries in peer-to-peer systems. In: CIDR, vol 3, pp 141–151

  10. Harvey NJ, Jones MB, Saroiu S, Theimer M, Wolman A (2003) Skipnet: a scalable overlay network with practical locality properties, WA, USA

  11. Li D, Cao J, Lu X, Chan K (2009) Efficient range query processing in peer-to-peer systems. Knowledge and Data Engineering. IEEE Trans 21(1):78–91

    Google Scholar 

  12. Li D, Lu X, Wu J (2005) Fissione: a scalable constant degree and low congestion dht scheme based on kautz graphs. In: INFOCOM 2005. 24Th annual joint conference of the IEEE computer and communications societies. Proceedings IEEE, vol 3. IEEE, pp 1677–1688

  13. Ratnasamy S, Francis P, Handley M, Karp R, Shenker S (2001) A scalable content-addressable network, vol. 31 ACM

  14. Ratnasamy S, Stoica I, Shenker S (2002) Routing algorithms for dhts: Some open questions. In: Peer-to-peer systems. Springer, pp 45–52

  15. Rowstron A, Druschel P (2001) Pastry: scalable, decentralized object location, and routing for large-scale peer-to-peer systems. In: Middleware 2001. Springer, pp 329–350

  16. Samet H (2006) Foundations of multidimensional and metric data structures Morgan Kaufmann

  17. Schmidt C, Parashar M (2004) Enabling flexible queries with guarantees in p2p systems. IEEE Internet Comput 8(3):19–26

    Article  Google Scholar 

  18. Shu Y, Ooi BC, Tan KL, Zhou A (2005) Supporting multi-dimensional range queries in peer-to-peer systems. In: Fifth IEEE international conference on Peer-to-peer computing, 2005. p2p 2005. IEEE, pp 173–180

  19. Simion R (2000) Noncrossing partitions. Discr Math 217(1): 367–409

    Article  MathSciNet  MATH  Google Scholar 

  20. Stoica I, Morris R, Karger D, Kaashoek MF, Balakrishnan H (2001) Chord: a scalable peer-to-peer lookup service for internet applications. ACM SIGCOMM Comput Commun Rev 31(4):149–160

    Article  Google Scholar 

  21. Tsatsanifos G, Sacharidis D, Sellis T (2011) Midas: multi-attribute indexing for distributed architecture systems. In: Advances in spatial and temporal databases. Springer, pp 168–185

  22. Zatloukal KC, Harvey NJ (2004) Family trees: an ordered dictionary with optimal congestion, locality, degree, and search time. In: Proceedings of the fifteenth annual ACM-SIAM symposium on discrete algorithms. Society for industrial and applied mathematics, pp 308–317

  23. Zhang Y, Lu X, Li D (2011) Survey of dht topology construction techniques in virtual computing environments. Sc China Inf Sci 54(11):2221–2235

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhao BY, Huang L, Stribling J, Rhea SC, Joseph AD, Kubiatowicz JD (2004) Tapestry: A resilient global-scale overlay for service deployment. IEEE J Sel Areas Commun 22(1):41–53

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by a Natural Sciences and Engineering Research (NSERC) Discovery Grant, number 36866-2011-RGPIN.

Author information

Authors and Affiliations

  1. Citi Bank, 5900 Hurontario Street, Mississauga, Ontario, L5R 0B8, Canada

    Pouya Bisadi

  2. Faculty of Computer Science, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada

    Zahra Mirikharaji & Bradford G. Nickerson

Authors
  1. Pouya Bisadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zahra Mirikharaji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bradford G. Nickerson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bradford G. Nickerson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bisadi, P., Mirikharaji, Z. & Nickerson, B.G. A fault tolerant peer-to-peer spatial data structure. Peer-to-Peer Netw. Appl. 10, 874–886 (2017). https://doi.org/10.1007/s12083-016-0436-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12083-016-0436-5

Keywords

Search

Navigation