Collaboration Without Communication: Evacuating Two Robots from a Disk

  • Sebastian Brandt
  • Felix Laufenberg
  • Yuezhou Lv
  • David Stolz
  • Roger Wattenhofer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10236)

Abstract

We consider the problem of evacuating two robots from a bounded area, through an unknown exit located on the boundary. Initially, the robots are in the center of the area and throughout the evacuation process they can only communicate with each other when they are at the same point at the same time. Having a visibility range of 0, the robots can only identify the location of the exit if they are already at the exit position. The task is to minimize the time it takes until both robots reach the exit, for a worst-case placement of the exit. For unit disks, an upper bound of 5.628 for the evacuation time is presented in [8]. Using the insight that, perhaps surprisingly, a forced meeting of the two robots as performed in the respective algorithm does not provide an exchange of any non-trivial information, we design a simpler algorithm that achieves an upper bound of 5.625. Our numerical simulations suggest that this bound is optimal for the considered natural class of algorithms. For dealing with the technical difficulties in analyzing the algorithm, we formulate a powerful new criterion that, for a given algorithm, reduces the number of possible worst-case exits radically. This criterion is of independent interest and can be applied to any area shape. Due to space restrictions, this version of the paper contains no proofs or illustrating figures; the full version can be found at http://disco.ethz.ch/publications/ciac2017-robotevac.pdf.

References

  1. 1.
    Alpern, S.: The rendezvous search problem. SIAM J. Control Optim. 33(3), 673–683 (1995)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Baeza-Yates, R.A., Culberson, J.C., Rawlins, G.J.E.: Searching with uncertainty extended abstract. In: Karlsson, R., Lingas, A. (eds.) SWAT 1988. LNCS, vol. 318, pp. 176–189. Springer, Heidelberg (1988). doi:10.1007/3-540-19487-8_20 Google Scholar
  3. 3.
    Beck, A., Newman, D.J.: Yet more on the linear search problem. Isr. J. Math. 8(4), 419–429 (1970)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Borowiecki, P., Das, S., Dereniowski, D., Kuszner, Ł.: Distributed evacuation in graphs with multiple exits. In: Suomela, J. (ed.) SIROCCO 2016. LNCS, vol. 9988, pp. 228–241. Springer, Cham (2016). doi:10.1007/978-3-319-48314-6_15 CrossRefGoogle Scholar
  5. 5.
    Chrobak, M., Gasieniec, L., Gorry, T., Martin, R.: Group search on the line. In: Italiano, G.F., Margaria-Steffen, T., Pokorný, J., Quisquater, J.-J., Wattenhofer, R. (eds.) SOFSEM 2015. LNCS, vol. 8939, pp. 164–176. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46078-8_14 Google Scholar
  6. 6.
    Czyzowicz, J., Dobrev, S., Georgiou, K., Kranakis, E., MacQuarrie, F.: Evacuating two robots from multiple unknown exits in a circle. In: ICDCN (2016). doi:10.1145/2833312.2833318
  7. 7.
    Czyzowicz, J., Gasieniec, L., Gorry, T., Kranakis, E., Martin, R., Pajak, D.: Evacuating robots via unknown exit in a disk. In: Kuhn, F. (ed.) DISC 2014. LNCS, vol. 8784, pp. 122–136. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45174-8_9 Google Scholar
  8. 8.
    Czyzowicz, J., Georgiou, K., Kranakis, E., Narayanan, L., Opatrny, J., Vogtenhuber, B.: Evacuating robots from a disk using face-to-face communication (extended abstract). In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 140–152. Springer, Cham (2015). doi:10.1007/978-3-319-18173-8_10 CrossRefGoogle Scholar
  9. 9.
    Czyzowicz, J., Kranakis, E., Krizanc, D., Narayanan, L., Opatrny, J., Shende, S.: Wireless autonomous robot evacuation from equilateral triangles and squares. In: Papavassiliou, S., Ruehrup, S. (eds.) ADHOC-NOW 2015. LNCS, vol. 9143, pp. 181–194. Springer, Cham (2015). doi:10.1007/978-3-319-19662-6_13 CrossRefGoogle Scholar
  10. 10.
    Dessmark, A., Fraigniaud, P., Pelc, A.: Deterministic rendezvous in graphs. In: Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 184–195. Springer, Heidelberg (2003). doi:10.1007/978-3-540-39658-1_19 CrossRefGoogle Scholar
  11. 11.
    Emek, Y., Langner, T., Stolz, D., Uitto, J., Wattenhofer, R.: How many ants does it take to find the food? In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 263–278. Springer, Cham (2014). doi:10.1007/978-3-319-09620-9_21 Google Scholar
  12. 12.
    Feinerman, O., Korman, A.: Memory lower bounds for randomized collaborative search and implications for biology. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 61–75. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33651-5_5 CrossRefGoogle Scholar
  13. 13.
    Feinerman, O., Korman, A., Lotker, Z., Sereni, J.-S.: Collaborative search on the plane without communication. In: PODC (2012). doi:10.1145/2332432.2332444
  14. 14.
    Förster, K.-T., Nuridini, R., Uitto, J., Wattenhofer, R.: Lower bounds for the capture time: linear, quadratic, and beyond. In: Scheideler, C. (ed.) Structural Information and Communication Complexity. LNCS, vol. 9439, pp. 342–356. Springer, Cham (2015). doi:10.1007/978-3-319-25258-2_24 CrossRefGoogle Scholar
  15. 15.
    Förster, K.-T., Wattenhofer, R.: Directed graph exploration. In: Baldoni, R., Flocchini, P., Binoy, R. (eds.) OPODIS 2012. LNCS, vol. 7702, pp. 151–165. Springer, Heidelberg (2012). doi:10.1007/978-3-642-35476-2_11 CrossRefGoogle Scholar
  16. 16.
    Fraigniaud, P., Ilcinkas, D., Peer, G., Pelc, A., Peleg, D.: Graph exploration by a finite automaton. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 451–462. Springer, Heidelberg (2004). doi:10.1007/978-3-540-28629-5_34 CrossRefGoogle Scholar
  17. 17.
    Kranakis, E., Krizanc, D., Rajsbaum, S.: Mobile agent rendezvous: a survey. In: Flocchini, P., Gasieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 1–9. Springer, Heidelberg (2006). doi:10.1007/11780823_1 CrossRefGoogle Scholar
  18. 18.
    Lamprou, I., Martin, R., Schewe, S.: Fast two-robot disk evacuation with wireless communication. In: Gavoille, C., Ilcinkas, D. (eds.) DISC 2016. LNCS, vol. 9888, pp. 1–15. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53426-7_1 CrossRefGoogle Scholar
  19. 19.
    Megow, N., Mehlhorn, K., Schweitzer, P.: Online graph exploration: new results on old and new algorithms. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 478–489. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22012-8_38 CrossRefGoogle Scholar
  20. 20.
    Nowakowski, R.J., Winkler, P.: Vertex-to-vertex pursuit in a graph. Discret. Math. 43(2–3), 235–239 (1983). doi:10.1016/0012-365X(83)90160-7 MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Parsons, T.D.: Pursuit-evasion in a graph. In: Alavi, Y., Lick, D.R. (eds.) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol. 642, pp. 426–441. Springer, Heidelberg (1978)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sebastian Brandt
    • 1
  • Felix Laufenberg
    • 1
  • Yuezhou Lv
    • 2
  • David Stolz
    • 1
  • Roger Wattenhofer
    • 1
  1. 1.ETH ZürichZürichSwitzerland
  2. 2.Tsinghua UniversityBeijingChina

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