Skip to main content
SpringerLink
Log in

Distributed Computing in Monotone Topological Spaces

  • Conference paper
  • First Online:
Beyond Databases, Architectures and Structures. Advanced Technologies for Data Mining and Knowledge Discovery (BDAS 2015, BDAS 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 613))

  • 1139 Accesses

Abstract

In recent times, an alternate approach to model and analyze distributed computing systems has gained research attention. The alternate approach considers higher-dimensional topological spaces and homotopy as well as homology while modeling and analyzing asynchronous distributed computing. This paper proposes that the monotone spaces having ending property can be effectively employed to model and analyze consistency and convergence of distributed computing. A set of definitions and analytical properties are constructed considering monotone spaces. The inter-space relationship between simplexes and monotone in topological spaces is formulated.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Armstrong, M.A.: Basic Topology. Springer, Berlin (1983)

    Book  MATH  Google Scholar 

  2. Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: The 25th Annual ACM Symposium on Theory of Computing. ACM (1993)

    Google Scholar 

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

    Google Scholar 

  4. Carson, S.D., Reynolds, J.P.F.: The geometry of semaphore programs. ACM Trans. Program. Lang. Syst. 9(1), 25–53 (1987)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. 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)

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  11. Herlihy, M., Rajsbaum, S.: New perspectives in distributed computing. In: Kutyłowski, M., Wierzbicki, T.M., Pacholski, L. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 170–186. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  12. Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46, 858–923 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. 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 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju, 660-701, 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

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Bagchi, S. (2016). Distributed Computing in Monotone Topological Spaces. In: Kozielski, S., Mrozek, D., Kasprowski, P., Małysiak-Mrozek, B., Kostrzewa, D. (eds) Beyond Databases, Architectures and Structures. Advanced Technologies for Data Mining and Knowledge Discovery. BDAS BDAS 2015 2016. Communications in Computer and Information Science, vol 613. Springer, Cham. https://doi.org/10.1007/978-3-319-34099-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-34099-9_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34098-2

  • Online ISBN: 978-3-319-34099-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation