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Hexagonal Bravais–Miller Routing by Cellular Automata Agents

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Parallel Computing Technologies (PaCT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9251))

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Abstract

This paper describes an efficient novel router in which the messages are transported by cellular automata (CA) agents. In order to implement agents more efficiently, the CA-w model (with write access) is used. The router is based upon a “Bravais–Miller” algorithm with hexagonal coordinates that explores the symmetries in the triangular lattice to provide a simple, deterministic, minimal routing scheme. As in a previous work, it uses henceforth six channels per node with at most one agent per channel so that one cell can host up to six agents. Each agent in a channel has a computed minimal direction defining the new channel in the adjacent node. In order to increase the throughput an adaptive routing protocol is defined, preferring the direction to an unoccupied channel. A strategy of deadlock avoidance is also investigated, from which the agent’s direction can dynamically be randomized.

D. Désérable—Until 2013.

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Notes

  1. 1.

    An equivalent symmetric protocol would be “first dirL then dirR”.

  2. 2.

    Except a homeomorphism.

  3. 3.

    Except special deadlock or livelock situations pointed out in Sect. 4.

References

  1. Woolridge, M., Jenning, N.R.: Intelligent agents: theory and practice. Knowl. Eng. Rev. 10(2), 115–152 (1995)

    Article  Google Scholar 

  2. Franklin, S., Graesser, A.: Is it an agent, or just a program?: a taxonomy for autonomous agents. In: Jennings, Nicholas R., Wooldridge, Michael J., Müller, Jörg P. (eds.) ECAI-WS 1996 and ATAL 1996. LNCS, vol. 1193. Springer, Heidelberg (1997)

    Google Scholar 

  3. Holland, J.H., Emergence: From chaos to order, Perseus Book (1998)

    Google Scholar 

  4. Woolridge, M.: An Introduction to Multiagent Systems. Wiley & Sons, New York (2002)

    Google Scholar 

  5. Pais, D.: Emergent collective behavior in multi-agent systems: an evolutionary perspective, PhD Dissertation. Princeton University, Princeton NJ (2012)

    Google Scholar 

  6. Schweitzer, F.: Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences. Springer Series in Synergetics. Springer, Heidelberg (2003)

    Google Scholar 

  7. Hoffmann, R.: The GCA-w massively parallel model. In: Malyshkin, V. (ed.) PaCT 2009. LNCS, vol. 5698, pp. 194–206. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Hoffmann, R.: GCA-w: global cellular automata with write-access. Acta Phys. Polonica B Proc. Suppl. 3(2), 347–364 (2010)

    Google Scholar 

  9. Hoffmann, R., Désérable, D.: Routing by cellular automata agents in the triangular lattice. In: Sirakoulis, G., Adamatzky, A. (eds.) Robots and Lattice Automata. Emergence, Complexity and Computation, pp. 117–147. Springer, Switzerland (2015)

    Google Scholar 

  10. Loh, P.K.K., Prakash, E.C.: Performance simulations of moving target search algorithms. Int. J. Comp. Games Tech. 3, 1–6 (2009)

    Article  Google Scholar 

  11. Korf, R.E.: Real-time heuristic search. Artif. Intell. 42(2–3), 189–211 (1990)

    Article  MATH  Google Scholar 

  12. Ediger, P., Hoffmann, R.: CA models for target searching agents. São José dos Campos ENTCS 252(2009), 41–54 (2009)

    MathSciNet  Google Scholar 

  13. Ediger, P., Hoffmann, R.: Routing based on evolved agents. In: 23rd PARS Workshop on Parallel System and Algorithms, ARCS, Hannover, Germany, pp. 45–53 (2010)

    Google Scholar 

  14. Ediger, P.: Modellierung und Techniken zur Optimierung von Multiagentensystemen in Zellularen Automaten, Dissertation, TU Darmstadt, Darmstadt, Germany (2011)

    Google Scholar 

  15. Hoffmann, R., Désérable, D.: Efficient minimal routing in the triangular grid with six channels. In: Malyshkin, V. (ed.) PaCT 2011. LNCS, vol. 6873, pp. 152–165. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Ediger, P., Hoffmann, R., Désérable, D.: Routing in the triangular grid with evolved agents. J. Cellular Automata 7(1), 47–65 (2012)

    MATH  Google Scholar 

  17. Ediger, P., Hoffmann, R., Désérable, D.: Rectangular vs triangular routing with evolved agents. J. Cellular Automata 8(1–2), 73–89 (2013)

    Google Scholar 

  18. Désérable, D.: A family of Cayley graphs on the hexavalent grid. Discrete Appl. Math. 93(2–3), 169–189 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Désérable, D.: Systolic dissemination in the arrowhead family. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2014. LNCS, vol. 8751, pp. 75–86. Springer, Heidelberg (2014)

    Google Scholar 

  20. Dally, W.J., Seitz, C.L.: The Torus routing chip. Dist. Comp. 1, 187–196 (1986)

    Article  Google Scholar 

  21. Xiang, Y., Stewart, I.A.: Augmented \(k\)-ary \(n\)-cubes. Inf. Sci. 181(1), 239–256 (2011)

    Article  MathSciNet  Google Scholar 

  22. Miller, W.H.: A Treatise on crystallography. J. & J.J. Deighton, London (1839)

    Google Scholar 

  23. Buerger, M.J.: Introduction to Crystal Geometry. McGraw-Hill, New York (1971)

    Google Scholar 

  24. Désérable, D.: Minimal routing in the triangular grid and in a family of related tori. In: Lengauer, Christian, Griebl, Martin, Gorlatch, Sergei (eds.) Euro-Par 1997. LNCS, vol. 1300. Springer, Heidelberg (1997)

    Google Scholar 

  25. Désérable, D.: Hexagonal Bravais-Miller routing of shortest path, IR#CU13220.1, pp. 1–15 (2013) – Désérable, D., Dumont, E.: Routing algorithm in torus T6n, IR#CU13220.2, pp. 1–8 (2013)

    Google Scholar 

  26. Désérable, D.: Arrowhead and diamond diameters, (submitted to Discrete Applied Math. & Applications)

    Google Scholar 

  27. Duato, J., Yalamanchili, S., Ni, L.: Interconnection Networks, Morgan Kaufmann (2002)

    Google Scholar 

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Authors and Affiliations

  1. Institut National des Sciences Appliquées, 20 Avenue des Buttes de Coësmes, 35043, Rennes, France

    Dominique Désérable

  2. Technische Universität Darmstadt, FB Informatik, FG Rechnerarchitektur, Hochschulstraße 10, 64289, Darmstadt, Germany

    Rolf Hoffmann

Authors
  1. Dominique Désérable
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  2. Rolf Hoffmann
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Correspondence to Dominique Désérable .

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Editors and Affiliations

  1. Russian Academy of Sciences, Novosibirsk, Russia

    Victor Malyshkin

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Désérable, D., Hoffmann, R. (2015). Hexagonal Bravais–Miller Routing by Cellular Automata Agents. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2015. Lecture Notes in Computer Science(), vol 9251. Springer, Cham. https://doi.org/10.1007/978-3-319-21909-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-21909-7_16

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