Skip to main content
SpringerLink
Log in

Lattice Based Consistent Slicer and Topological Cut for Distributed Computation in Monotone Spaces

  • Conference paper
  • First Online:
Beyond Databases, Architectures and Structures. Towards Efficient Solutions for Data Analysis and Knowledge Representation (BDAS 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 716))

  • 1253 Accesses

Abstract

The distributed database systems are increasingly employing distributed systems platforms for data deployment and query based computation. The models of distributed systems play a role in determining data partitioning and placement in distributed database systems. The applications of concepts of topological spaces are gaining research attention for modeling structures of distributed systems. In a distributed system, the slicer of distributed computation partitions a set of processes into subsets maintaining consistency property. In this paper, a lattice based slicer model of distributed computation is presented considering monotone topological spaces. The model considers state-space of asynchronous distributed computation. The proposed monotone slicer model of computation preserves the lattice cover of Birkhoff’s representation. A set of analytical properties of the monotone slicer model is formulated. Furthermore, the topological cut of an event-based asynchronous distributed computation is formulated as a set of axioms.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alpern, B., Schneider, F.B.: Defining liveness. Inf. Process. Lett. 21(4), 181–185 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bauer, U., Kerber, M., Reininghaus, J.: Distributed computation of persistent homology. In: Proceedings of Meeting on Algorithm Engineering and Experiments, SIAM, pp. 31–38 (2014)

    Google Scholar 

  3. Bliss, T.N., Kepner, J.: pMatlab parallel Matlab library. Int. J. High Perform. Comput. Appl. 21(3), 336–359 (2007)

    Article  Google Scholar 

  4. Borowsky, E., Gafni, E.: A simple algorithmically reasoned characterization of wait-free computation. In: Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, pp. 189–198 (1997)

    Google Scholar 

  5. Conde, R., Rajsbaum, S.: An introduction to topological theory of distributed computing with safe-consensus. Electron. Notes Theor. Comput. Sci. 283, 29–51 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Duarte, C.H.C.: Mathematical models of object-based distributed systems. In: Agha, G., Danvy, O., Meseguer, J. (eds.) Talcott Festschrift. LNCS, vol. 7000, pp. 57–73. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24933-4_4

    Chapter  Google Scholar 

  7. Fajstrup, L., Rauben, M., Goubault, E.: Algebraic topology and concurrency. Theoret. Comput. Sci. 357(1–3), 241–278 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fraigniaud, P., Rajsbaum, S., Travers, C.: Locality and checkability in wait-free computing. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 333–347. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24100-0_34

    Chapter  Google Scholar 

  9. Ghosh, S.R., Dasgupta, H.: Connectedness in monotone spaces. Bull. Malays. Math. Sci. Soc. 27(2), 129–148 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Goubault, E.: Some geometric perspectives in concurrency theory. Homol. Homotopy Appl. 5(2), 95–136 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Goubault, E., Jensen, T.P.: Homology of higher dimensional automata. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 254–268. Springer, Heidelberg (1992). doi:10.1007/BFb0084796

    Google Scholar 

  12. Gramoli, V., et al.: Slicing distributed systems. IEEE Trans. Comput. 58(11), 1444–1455 (2009)

    Article  MathSciNet  Google Scholar 

  13. Gunawardena, J.: Homotopy and concurrency. Bull. EATCS 54, 184–193 (1994)

    MATH  Google Scholar 

  14. Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Elsevier, Amsterdam (2014)

    MATH  Google Scholar 

  15. Herlihy, M., Rajsbaum, S.: New perspectives in distributed computing. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 170–186. Springer, Heidelberg (1999). doi:10.1007/3-540-48340-3_16

    Chapter  Google Scholar 

  16. Hoest, G., Shavit, N.: Toward a topological characterization of asynchronous complexity. SIAM J. Comput. 36(2), 457–497 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Huang, Y., Yesha, Y., Zhou, S.: A database based distributed computation architecture with Accumulo and D4M: an application of eigensolver for large sparse matrix. In: IEEE International Conference on Big Data (2015)

    Google Scholar 

  18. Kepner, J.: Massive database analysis on the cloud with D4M. In: Proceedings of HPEC Workshop (2011)

    Google Scholar 

  19. Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: the topology of public knowledge. SIAM J. Comput. 29(5), 1449–1483 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zomorodian, A., Carlsson, G.: Computing persistent homology. Discret. Comput. Geom. 33(2), 249–274 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju, South Korea

    Susmit Bagchi

Authors
  1. Susmit Bagchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Susmit Bagchi .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Stanisław Kozielski

  2. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Dariusz Mrozek

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Paweł Kasprowski

  4. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Bożena Małysiak-Mrozek

  5. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Daniel Kostrzewa

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Bagchi, S. (2017). Lattice Based Consistent Slicer and Topological Cut for Distributed Computation in Monotone Spaces. In: Kozielski, S., Mrozek, D., Kasprowski, P., Małysiak-Mrozek, B., Kostrzewa, D. (eds) Beyond Databases, Architectures and Structures. Towards Efficient Solutions for Data Analysis and Knowledge Representation. BDAS 2017. Communications in Computer and Information Science, vol 716. Springer, Cham. https://doi.org/10.1007/978-3-319-58274-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-58274-0_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58273-3

  • Online ISBN: 978-3-319-58274-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation