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The topology of look-compute-move robot wait-free algorithms with hard termination

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Abstract

Look-Compute-Move models for a set of autonomous robots have been thoroughly studied for over two decades. We consider the standard Asynchronous Luminous Robots (ALR) model, where robots are located in a graph G. Each robot, repeatedly Looks at its surroundings and obtains a snapshot containing the vertices of G, where all robots are located; based on this snapshot, each robot Computes a vertex (adjacent to its current position), and then Moves to it. Robots have visible lights, allowing them to communicate more information than only its actual position, and they move asynchronously, meaning that each one runs at its own arbitrary speed. We are also interested in a case which has been barely explored: the robots need not all be present initially, they might appear asynchronously. We call this the Extended Asynchronous Appearing Luminous Robots (EALR) model. A central problem in the mobile robots area is bringing the robots to the same vertex. We study several versions of this problem, where the robots move towards the same (or close to each other) vertices. And we concentrate on the requirement that each robot executes a finite number of Look-Compute-Move cycles, independently of the interleaving of other robot’s cycles, and then stops. Our main result is direct connections between the (ALR and) EALR model and the asynchronous wait-free multiprocess read/write shared memory (WFSM) model. General robot tasks in a graph are also provided, which include several version of gathering. Finally, using the connection between the EALR model and the WFSM model, a combinatorial topology characterization for the solvable robot tasks is presented.

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Notes

  1. We could have instead assumed that a process can only atomically read individually shared registers because it is known that is possible to implement an atomic Snapshot in a wait-free manner from read and write operations (see for example [36, 37]).

  2. Note that with this modification it is straightforward to model systems where all robots are initially visible since the beginning of the execution: the light of every robot is initialized merely to a non-negative value, for example, 0.

  3. In the Strong version of the EARL, we assume that robots are non-oblivious, non-anonymous, non-disoriented, share the same labeling of G and can detect multiplicities.

References

  1. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, San Francisco, CA (2013)

    MATH  Google Scholar 

  4. Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory, vol. 3(2). Morgan & Claypool, San Rafael (2012)

    MATH  Google Scholar 

  5. Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Hard Tasks for Weak Robots: The Role of Common Knowledge in Pattern Formation by Autonomous Mobile Robots, LNCS, vol. 1741, pp. 93–102. Springer, Berlin (1999)

    MATH  Google Scholar 

  6. Asaf, E., Peleg, D.: Distributed models and algorithms for mobile robot systems. In: 33rd Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), LNCS, vol. 4362, pp. 70–87. Springer (2007)

  7. Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: Autonomous mobile robots with lights. Theor. Comput. Sci. 609(P1), 171–184 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. D’Emidio, M., Frigioni, D., Navarra, A.: Synchronous robots vs asynchronous lights-enhanced robots on graphs. In: Electronic Notes in Theoretical Computer Science. Proceedings of ICTCS 2015, the 16th Italian Conference on Theoretical Computer Science, vol. 322, pp. 169–180 (2016)

  9. Yu, X., Yung, M.: Agent rendezvous: a dynamic symmetry-breaking problem. In: Automata, Languages and Programming, 23rd International Colloquium, ICALP96, Paderborn, Germany, 8–12 July 1996, Proceedings, LNCS, vol. 1099, pp. 610–621. Springer (1996)

  10. Potop-Butucaru, M., Raynal, M., Tixeuil, S.: Distributed computing with mobile robots: an introductory survey. In: 2011 14th International Conference on Network-Based Information Systems (NBiS), pp. 318–324 (2011)

  11. Prencipe, G.: Autonomous mobile robots: a distributed computing perspective. In: 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS), LNCS, vol. 8243, pp. 6–21. Springer (2014)

  12. Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. In: Theoretical Computer Science, Structural Information and Communication Complexity (SIROCCO 2005), vol. 384(2), pp. 222–231 (2007)

  13. Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337(1), 147–168 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Cieliebak, M.: Gathering non-oblivious mobile robots. In: Farach-Colton, M. (ed.) LATIN 2004: Theoretical Informatics, pp. 577–588. Springer, Berlin (2004)

    Chapter  Google Scholar 

  16. Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390(1), 27–39 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Bonnet, F., Potop-Butucaru, M., Tixeuil, S.: Asynchronous gathering in rings with 4 robots. In: Proceedings of Ad-hoc, Mobile, and Wireless Networks: 15th International Conference (ADHOC-NOW), LNCS, vol. 9724, pp. 311–324. Springer (2016)

  19. D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering on rings under the look-compute-move model. Distrib. Comput. 27(4), 255–285 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Rendezvous with constant memory. Theor. Comput. Sci. 621, 57–72 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. Viglietta, G.: Rendezvous of two robots with visible bits. In: 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, LNCS, vol. 8243, pp. 291–306. Springer (2014)

  22. D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids without multiplicity detection. In: Even, G., Halldórsson, M.M. (eds.) Structural Information and Communication Complexity, pp. 327–338. Springer, Berlin (2012)

    Chapter  Google Scholar 

  23. D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering Asynchronous and Oblivious Robots on Basic Graph Topologies Under the Look-Compute-Move Model, pp. 197–222. Springer, New York (2013)

    MATH  Google Scholar 

  24. Izumi, T., Souissi, S., Katayama, Y., Inuzuka, N., Défago, X., Wada, K., Yamashita, M.: The gathering problem for two oblivious robots with unreliable compasses. CoRR, arXiv:1111.1492 (2011)

  25. Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput. 36(1), 56–82 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  26. Bouzid, Z., Das, S., Tixeuil, S.: Gathering of mobile robots tolerating multiple crash faults. In: IEEE 33rd International Conference on Distributed Computing Systems (ICDCS), pp. 337–346. IEEE Computer Society, Washington, DC, USA (2013)

  27. Bramas, Q., Tixeuil, S.: Wait-free gathering without chirality. In: 22nd Structural Information and Communication Complexity (SIROCCO), LNCS, vol. 9439, pp. 313–327. Springer (2015)

  28. Castañeda, A., Rajsbaum, S., Roy, M.: Two convergence problems for robots on graphs. In: 2016 Seventh Latin-American Symposium on Dependable Computing, LADC 2016, Cali, Colombia, October 19–21, 2016, pp. 81–90. IEEE Computer Society (2016)

  29. Herlihy, M., Rajsbaum, S.: A classification of wait-free loop agreement tasks. Theor. Comput. Sci. 291(1), 55–77 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  30. De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theor. Comput. Sci. 355(3), 315–326 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Dessmark, A., Fraigniaud, P., Kowalski, D.R., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46(1), 69–96 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  32. Bouchard, S., Dieudonné, Y., Ducourthial, B.: Byzantine gathering in networks. Distrib. Comput. 29(6), 435–457 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Dieudonné, Y., Pelc, A., Peleg, D.: Gathering despite mischief. ACM Trans. Algorithms 11(1), 1:1–1:28 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chalopin, J., Dieudonné, Y., Labourel, A., Pelc, A.: Fault-tolerant rendezvous in networks. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) Automata, Languages, and Programming, pp. 411–422. Springer, Berlin (2014)

    Google Scholar 

  35. Agathangelou, C., Georgiou, C., Mavronicolas, M.: A distributed algorithm for gathering many fat mobile robots in the plane. In: ACM Symposium on Principles of Distributed Computing, PODC ’13, Montreal, QC, Canada, July 22–24, 2013, pp. 250–259 (2013)

  36. Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics. Wiley, Hoboken (2004)

    Book  MATH  Google Scholar 

  37. Raynal, M.: Safe, Regular, and Atomic Read/Write Registers, pp. 305–328. Springer, Berlin (2013)

    Google Scholar 

  38. Bose, K., Adhikary, R., Chaudhuri, S.G., Sau, B.: Crash tolerant gathering on grid by asynchronous oblivious robots. CoRR, arXiv:1709.00877 (2017)

  39. Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC), pp. 91–100 (1993)

  40. Borowsky, E., Gafni, E., Lynch, N., Rajsbaum, S.: The BG distributed simulation algorithm. Distrib. Comput. 14(3), 127–146 (2001)

    Article  Google Scholar 

  41. Chaudhuri, S.: More choices allow more faults: set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  42. Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  43. Gafni, E., Koutsoupias, E.: Three-processor tasks are undecidable. SIAM J. Comput. 28(3), 970–983 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  44. Herlihy, M., Rajsbaum, S.: The decidability of distributed decision tasks (extended abstract). In: Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing (STOC), pp. 589–598 (1997)

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Acknowledgements

David Flores-Peñaloza, Sergio Rajsbaum and Armando Castañeda are supported by Universidad Nacional Autónoma de México, PAPIIT Projects IN117317, IN109917 and IA102417, respectively. Part of this work was done while Sergio Rajsbaum was at Ecole Polytechnic and U. Paris 7. We thank the referees for their valuable comments.

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Authors and Affiliations

  1. Facultad de Ciencias, UNAM, 04510, Mexico City, Mexico

    Manuel Alcántara & David Flores-Peñaloza

  2. Instituto de Matemáticas, UNAM, 04510, Mexico City, Mexico

    Armando Castañeda & Sergio Rajsbaum

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  1. Manuel Alcántara
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Correspondence to Manuel Alcántara.

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Alcántara, M., Castañeda, A., Flores-Peñaloza, D. et al. The topology of look-compute-move robot wait-free algorithms with hard termination. Distrib. Comput. 32, 235–255 (2019). https://doi.org/10.1007/s00446-018-0345-3

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