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International Workshop on Approximation and Online Algorithms

WAOA 2017: Approximation and Online Algorithms pp 223–237Cite as

On-line Search in Two-Dimensional Environment

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10787))

Abstract

We consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids: nodes are placed on the plane at integer coordinates and only nodes at distance one can be adjacent. We give an on-line algorithm for the searchers that allows them to compute a connected and monotone strategy that guarantees searching any unknown partial grid with the use of \(O(\sqrt{n})\) searchers, where n is the number of nodes in the grid. We prove also a lower bound of \(\varOmega (\sqrt{n}/\log n)\) in terms of achievable competitive ratio of any on-line algorithm.

Research partially supported by National Science Centre (Poland) grant number 2015/17/B/ST6/01887. The full version can be found at: https://arxiv.org/abs/1610.01458.

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Notes

  1. 1.

    In this work the terms graph and network are used exchangeably.

References

  1. Altshuler, Y., Yanovski, V., Wagner, I., Bruckstein, A.: Multi-agent cooperative cleaning of expanding domains. Int. J. Robot. Res. 30(8), 1037–1071 (2011)

    Article  Google Scholar 

  2. Barrière, L., Flocchini, P., Fomin, F., Fraigniaud, P., Nisse, N., Santoro, N., Thilikos, D.: Connected graph searching. Inf. Comput. 219, 1–16 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Best, M.J., Gupta, A., Thilikos, D.M., Zoros, D.: Contraction obstructions for connected graph searching. Discret. Appl. Math. (2015). https://doi.org/10.1016/j.dam.2015.07.036

  4. Bhadauria, D., Klein, K., Isler, V., Suri, S.: Capturing an evader in polygonal environments with obstacles: the full visibility case. Int. J. Robot. Res. 31(10), 1176–1189 (2012)

    Article  Google Scholar 

  5. Blin, L., Fraigniaud, P., Nisse, N., Vial, S.: Distributed chasing of network intruders. Theor. Comput. Sci. 399(1–2), 12–37 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Borowiecki, P., Dereniowski, D., Kuszner, L.: Distributed graph searching with a sense of direction. Distrib. Comput. 28(3), 155–170 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chung, T., Hollinger, G., Isler, V.: Search and pursuit-evasion in mobile robotics - a survey. Auton. Robots 31(4), 299–316 (2011)

    Article  Google Scholar 

  8. Daadaa, Y., Flocchini, P., Zaguia, N.: Network decontamination with temporal immunity by cellular automata. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds.) ACRI 2010. LNCS, vol. 6350, pp. 287–299. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15979-4_31

    Chapter  Google Scholar 

  9. Dereniowski, D.: Connected searching of weighted trees. Theor. Comput. Sci. 412, 5700–5713 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dereniowski, D.: Approximate search strategies for weighted trees. Theor. Comput. Sci. 463, 96–113 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dereniowski, D.: From pathwidth to connected pathwidth. SIAM J. Discret. Math. 26(4), 1709–1732 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Durham, J., Franchi, A., Bullo, F.: Distributed pursuit-evasion without mapping or global localization via local frontiers. Auton. Robot. 32(1), 81–95 (2012)

    Article  Google Scholar 

  13. Ellis, J., Warren, R.: Lower bounds on the pathwidth of some grid-like graphs. Discret. Appl. Math. 156(5), 545–555 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Flocchini, P., Huang, M., Luccio, F.: Decontamination of hypercubes by mobile agents. Networks 52(3), 167–178 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Flocchini, P., Luccio, F., Pagli, L., Santoro, N.: Optimal network decontamination with threshold immunity. In: Spirakis, P.G., Serna, M. (eds.) CIAC 2013. LNCS, vol. 7878, pp. 234–245. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38233-8_20

    Chapter  Google Scholar 

  16. Flocchini, P., Luccio, F., Pagli, L., Santoro, N.: Network decontamination under m-immunity. Discret. Appl. Math. 201, 114–129 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fomin, F., Thilikos, D.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Gonçalves, V.C.F., Lima, P.M.V., Maculan, N., França, F.M.G.: A distributed dynamics for webgraph decontamination. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6415, pp. 462–472. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16558-0_39

    Chapter  Google Scholar 

  19. Hollinger, G., Singh, S., Djugash, J., Kehagias, A.: Efficient multi-robot search for a moving target. Int. J. Robot. Res. 28(2), 201–219 (2009)

    Article  Google Scholar 

  20. Ilcinkas, D., Nisse, N., Soguet, D.: The cost of monotonicity in distributed graph searching. Distrib. Comput. 22(2), 117–127 (2009)

    Article  MATH  Google Scholar 

  21. Karaivanov, B., Markov, M., Snoeyink, J., Vassilev, T.: Decontaminating planar regions by sweeping with barrier curves. In: Proceedings of the 26th Canadian Conference on Computational Geometry, CCCG 2014 (2014)

    Google Scholar 

  22. Kolling, A., Carpin, S.: Multi-robot pursuit-evasion without maps. In: Proceedings of IEEE International Conference on Robotics and Automation, ICRA 2010, pp. 3045–3051 (2010)

    Google Scholar 

  23. LaPaugh, A.: Recontamination does not help to search a graph. J. ACM 40(2), 224–245 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  24. Markov, M., Haralampiev, V., Georgiev, G.: Lower bounds on the directed sweepwidth of planar shapes. Serdica J. Comput. 9(2), 151–166 (2015)

    MathSciNet  Google Scholar 

  25. Megiddo, N., Hakimi, S., Garey, M., Johnson, D., Papadimitriou, C.: The complexity of searching a graph. J. ACM 35(1), 18–44 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  26. Moraveji, R., Sarbazi-Azad, H., Zomaya, A.: Performance modeling of Cartesian product networks. J. Parallel Distrib. Comput. 71(1), 105–113 (2011)

    Article  MATH  Google Scholar 

  27. Parsons, T.D.: Pursuit-evasion in a graph. In: Alavi, Y., Lick, D.R. (eds.) Theory and Applications of Graphs. LNCS, vol. 642, pp. 426–441. Springer, Heidelberg (1978). https://doi.org/10.1007/BFb0070400

    Chapter  Google Scholar 

  28. Petrov, N.: A problem of pursuit in the absence of information on the pursued. Differ. Uravn. 18, 1345–1352 (1982)

    MathSciNet  Google Scholar 

  29. Robin, C., Lacroix, S.: Multi-robot target detection and tracking: taxonomy and survey. Auton. Robot. 40(4), 729–760 (2016)

    Article  Google Scholar 

  30. Sachs, S., LaValle, S., Rajko, S.: Visibility-based pursuit-evasion in an unknown planar environment. Int. J. Robot. Res. 23(1), 3–26 (2004)

    Article  Google Scholar 

  31. Stiffler, N., O’Kane, J.: A complete algorithm for visibility-based pursuit-evasion with multiple pursuers. In: Proceedings of the IEEE International Conference on Robotics and Automation, ICRA 2014, pp. 1660–1667 (2014)

    Google Scholar 

  32. Yang, B., Dyer, D., Alspach, B.: Sweeping graphs with large clique number. Discret. Math. 309(18), 5770–5780 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, 80-233, Gdańsk, Poland

    Dariusz Dereniowski & Dorota Urbańska

Authors
  1. Dariusz Dereniowski
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  2. Dorota Urbańska
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Correspondence to Dariusz Dereniowski .

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Editors and Affiliations

  1. The University of Western Ontario, London, Ontario, Canada

    Roberto Solis-Oba

  2. German University of Technology in Oman, Muscat, Oman

    Rudolf Fleischer

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Dereniowski, D., Urbańska, D. (2018). On-line Search in Two-Dimensional Environment. In: Solis-Oba, R., Fleischer, R. (eds) Approximation and Online Algorithms. WAOA 2017. Lecture Notes in Computer Science(), vol 10787. Springer, Cham. https://doi.org/10.1007/978-3-319-89441-6_17

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  • DOI: https://doi.org/10.1007/978-3-319-89441-6_17

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  • Online ISBN: 978-3-319-89441-6

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