Search on a Line by Byzantine Robots

Authors Jurek Czyzowicz, Konstantinos Georgiou, Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Jaroslav Opatrny, Sunil Shende



PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2016.27.pdf
  • Filesize: 466 kB
  • 12 pages

Document Identifiers

Author Details

Jurek Czyzowicz
Konstantinos Georgiou
Evangelos Kranakis
Danny Krizanc
Lata Narayanan
Jaroslav Opatrny
Sunil Shende

Cite AsGet BibTex

Jurek Czyzowicz, Konstantinos Georgiou, Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Jaroslav Opatrny, and Sunil Shende. Search on a Line by Byzantine Robots. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 27:1-27:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ISAAC.2016.27

Abstract

We consider the problem of fault-tolerant parallel search on an infinite line by n robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed 1 and can communicate in wireless mode among themselves. However, among the n robots, there are f robots that exhibit byzantine faults. A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient verification that the target has been found. We aim to design algorithms that minimize the value of S_d (n, f), the time to find a target at a distance d from the origin by n robots among which f are faulty. We give several different algorithms whose running time depends on the ratio f/n, the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.
Keywords
  • Cow path problem
  • Parallel search
  • Mobile robots
  • Wireless communication
  • Byzantine faults

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. N. Agmon and D. Peleg. Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM Journal on Computing, 36(1):56-82, 2006. Google Scholar
  2. S. Albers and M. R. Henzinger. Exploring unknown environments. SIAM Journal on Computing, 29(4):1164-1188, 2000. Google Scholar
  3. S. Albers, K. Kursawe, and S. Schuierer. Exploring unknown environments with obstacles. Algorithmica, 32(1):123-143, 2002. Google Scholar
  4. S. Alpern and S. Gal. The theory of search games and rendezvous, volume 55. Kluwer Academic Publishers, 2002. Google Scholar
  5. R. Baeza Yates, J. Culberson, and G. Rawlins. Searching in the plane. Information and Computation, 106(2):234-252, 1993. Google Scholar
  6. E. Bampas, J. Czyzowicz, L. Gasieniec, D. Ilcinkas, R. Klasing, T. Kociumaka, and D. Pajak. Linear search by a pair of distinct-speed robots. In SIROCCO. to appear, 2016. Google Scholar
  7. A. Beck. On the linear search problem. Israel J. of Mathematics, 2(4):221-228, 1964. Google Scholar
  8. A. Beck. More on the linear search problem. Israel J. of Mathematics, 3(2):61-70, 1965. Google Scholar
  9. A. Beck and M. Beck. Son of the linear search problem. Israel Journal of Mathematics, 48(2-3):109-122, 1984. Google Scholar
  10. A. Beck and D. Newman. Yet more on the linear search problem. Israel J. of Mathematics, 8(4):419-429, 1970. Google Scholar
  11. A. Beck and P. Warren. The return of the linear search problem. Israel J. of Mathematics, 14(2):169-183, 1973. Google Scholar
  12. R. Bellman. An optimal search. SIAM Review, 5(3):274-274, 1963. Google Scholar
  13. P. Bose and J.-L. De Carufel. A general framework for searching on a line. In WALCOM: Algorithms and Computation - 10th International Workshop, WALCOM 2016, Kathmandu, Nepal, March 29-31, 2016, Proceedings, pages 143-153, 2016. Google Scholar
  14. P. Bose, J.-L. De Carufel, and S. Durocher. Revisiting the problem of searching on a line. In Algorithms - ESA 2013 - 21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings, pages 205-216, 2013. Google Scholar
  15. A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro. Time-varying graphs and dynamic networks. In Ad-hoc, mobile, and wireless networks, LNCS, volume 6811, pages 346-359. Springer, 2011. Google Scholar
  16. M. Chrobak, L. Gasieniec, Gorry T., and R. Martin. Group search on the line. In SOFSEM 2015. Springer, 2015. Google Scholar
  17. R. Cohen and D. Peleg. Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM Journal of Computing, 41(1):1516-1528, 2005. Google Scholar
  18. J. Czyzowicz, L. Gasieniec, A. Kosowski, E. Kranakis, D. Krizanc, and N. Taleb. When patrolmen become corrupted: Monitoring a graph using faulty mobile robots. In Algorithms and Computation - Proceedings of 26th ISAAC 2015, pages 343-354, 2015. Google Scholar
  19. J. Czyzowicz, E. Kranakis, D. Krizanc, L. Narayanan, and Opatrny J. Search on a line with faulty robots. In PODC. ACM, 2016. Google Scholar
  20. E. D. Demaine, S. P. Fekete, and S. Gal. Online searching with turn cost. Theoretical Computer Science, 361(2):342-355, 2006. Google Scholar
  21. X. Deng, T. Kameda, and C. Papadimitriou. How to learn an unknown environment. In FOCS, pages 298-303. IEEE, 1991. Google Scholar
  22. Y. Dieudonné, A. Pelc, and D. Peleg. Gathering despite mischief. ACM Transactions on Algorithms (TALG), 11(1):1, 2014. Google Scholar
  23. F. V. Fomin and D. M. Thilikos. An annotated bibliography on guaranteed graph searching. Theoretical Computer Science, 399(3):236-245, 2008. Google Scholar
  24. F. Hoffmann, C. Icking, R. Klein, and K. Kriegel. The polygon exploration problem. SIAM Journal on Computing, 31(2):577-600, 2001. Google Scholar
  25. J. Hromkovič, R. Klasing, B. Monien, and R. Peine. Dissemination of information in interconnection networks (broadcasting &gossiping). In Combinatorial network theory, pages 125-212. Springer, 1996. Google Scholar
  26. J. Kleinberg. On-line search in a simple polygon. In SODA, page 8. SIAM, 1994. Google Scholar
  27. F. Kuhn, N. Lynch, and R. Oshman. Distributed computation in dynamic networks. In Proceedings of the forty-second ACM symposium on Theory of computing, pages 513-522. ACM, 2010. Google Scholar
  28. L. Lamport, R. Shostak, and M. Pease. The byzantine generals problem. ACM Transactions on Programming Languages and Systems (TOPLAS), 4(3):382-401, 1982. Google Scholar
  29. N. A. Lynch. Distributed algorithms. Morgan Kaufmann, 1996. Google Scholar
  30. C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. In ICALP, pages 610-620. Springer, 1989. Google Scholar
  31. S. Souissi, X. Défago, and M. Yamashita. Gathering asynchronous mobile robots with inaccurate compasses. Principles of Distributed Systems, pages 333-349, 2006. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail