Skip to main content

Automatic Synthesis of Optimal-Size Concentrators by Answer Set Programming

  • Conference paper
  • First Online:
Book cover Logic Programming and Nonmonotonic Reasoning (LPNMR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10377))

Abstract

A concentrator is a circuit with N inputs and \(M\le N\) outputs that can route any given subset of \(K\le M\) valid inputs to K of its M outputs. Concentrator circuits are important building blocks of many parallel algorithms. The design of optimal concentrator circuits is however a challenging task that has already been considered in many research papers. In this paper, we show how answer set programming can be used to automatically generate concentrator circuits of provably optimal size.

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

Access this chapter

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. Batcher, K.: Sorting networks and their applications. In: AFIPS Spring Joint Computer Conference, vol. 32, pp. 307–314 (1968)

    Google Scholar 

  2. Bundala, D., Codish, M., Cruz-Filipe, L., Schneider-Kamp, P., Závodný, J.: Optimal-depth sorting networks. J. Comput. Syst. Sci. 84, 185–204 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bundala, D., Závodný, J.: Optimal sorting networks. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 236–247. Springer, Cham (2014). doi:10.1007/978-3-319-04921-2_19

    Chapter  Google Scholar 

  4. Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F., Schaub, T.: ASP-Core-2 input language format, ASP Standardization Working Group, March 2013

    Google Scholar 

  5. Chung, F.: On concentrators, superconcentrators, generalizers, and nonblocking networks. Bell Syst. Tech. J. 58(8), 1765–1777 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. Codish, M., Cruz-Filipe, L., Ehlers, T., Müller, M., Schneider-Kamp, P.: Sorting networks: to the end and back again. Cornell University, July 2015. arXiv Report arXiv:1507.01428v1

  7. Ehlers, T., Müller, M.: New bounds on optimal sorting networks. Cornell University Library, January 2015. arXiv Report arXiv:1501.06946v1

  8. Eiter, T., Ianni, G., Krennwallner, T.: Answer set programming: a primer. In: Tessaris, S., Franconi, E., Eiter, T., Gutierrez, C., Handschuh, S., Rousset, M.-C., Schmidt, R.A. (eds.) Reasoning Web 2009. LNCS, vol. 5689, pp. 40–110. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03754-2_2

    Chapter  Google Scholar 

  9. Gabber, O., Galil, Z.: Explicit constructions of linear-sized superconcentrators. J. Comput. Syst. Sci. 22(3), 407–420 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: a conflict-driven answer set solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 260–265. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72200-7_23

    Chapter  Google Scholar 

  11. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set enumeration. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 136–148. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72200-7_13

    Chapter  Google Scholar 

  12. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Logic Programming, Seattle, Washington, USA, pp. 1070–1080. MIT Press (1988)

    Google Scholar 

  13. Jain, T., Schneider, K.: Verifying the concentration property of permutation networks by BDDs. In: Leonard, E., Schneider, K. (eds.) Formal Methods and Models for Codesign (MEMOCODE), Kanpur, India, pp. 43–53. IEEE Computer Society (2016)

    Google Scholar 

  14. Leone, N., Pfeifer, G., Faber, W., Calimeri, F., Dell’Armi, T., Eiter, T., Gottlob, G., Ianni, G., Ielpa, G., Koch, C., Perri, S., Polleres, A.: The DLV system. In: Flesca, S., Greco, S., Ianni, G., Leone, N. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 537–540. Springer, Heidelberg (2002). doi:10.1007/3-540-45757-7_50

    Chapter  Google Scholar 

  15. Morgenstern, A., Schneider, K.: Synthesis of parallel sorting networks using SAT solvers. In: Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (MBMV), Oldenburg, Germany, pp. 71–80 (2011)

    Google Scholar 

  16. Parberry, I.: The pairwise sorting network. Par. Proc. Lett. (PPL) 2(2–3), 205–211 (1992)

    Article  MathSciNet  Google Scholar 

  17. Pinsker, M.: On the complexity of a concentrator. In: International Teletraffic Conference (ITC), Stockholm, Sweden, pp. 318:1–318:4 (1973)

    Google Scholar 

  18. Quinton, B., Wilton, S.: Concentrator access networks for programmable logic cores on SoCs. In: International Symposium on Circuits and Systems (ISCAS), Kobe, Japan, vol. 1, pp. 45–48. IEEE Computer Society (2005)

    Google Scholar 

  19. Schöning, U.: Smaller superconcentrators of density 28. Inf. Process. Lett. (IPL) 98(4), 127–129 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marc Dahlem .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Dahlem, M., Jain, T., Schneider, K., Gillmann, M. (2017). Automatic Synthesis of Optimal-Size Concentrators by Answer Set Programming. In: Balduccini, M., Janhunen, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2017. Lecture Notes in Computer Science(), vol 10377. Springer, Cham. https://doi.org/10.1007/978-3-319-61660-5_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-61660-5_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61659-9

  • Online ISBN: 978-3-319-61660-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics