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Online Strategies for Evacuating from a Convex Region in the Plane

  • Songhua LiEmail author
  • Yinfeng Xu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

This paper studies an evacuation problem that evacuees inside an affected convex region in the plane try to escape to a boundary of the region as quickly as possible. The boundary information of the region is usually unknown to the evacuees at the beginning during an emergency. But with the help of helicopters or even satellite remote sensing technology, outside rescuers can easily get complete boundary information, and rescuers can share the information with evacuees once getting in touch with the evacuee who firstly reaches a boundary. For the scenario that people evacuate from several different positions, we first show that 3 is a lower bound on the competitive ratio, and present an online strategy with its competitive ratio proved to be no more than \( 2 + \sqrt 5 \). For the scenario that people evacuate from a single initial position, we present a strategy with its competitive ratio very close to the lower bound.

Keywords

Evacuation strategy Competitive analysis Convex region 

Notes

Acknowledgments

This research is partially supported by the NSFC (Grant No. 71601152), and by the China Postdoctoral Science Foundation (Grant No. 2016M592811).

References

  1. 1.
    Deng, X.T., Kameda, T., Papadimitriou, C.: How to learn an unknown environment I: the rectilinear case. J. ACM 45(2), 215–245 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Papadimitriou, C.H., Yannakakis, M.: Shortest path without a map. Theoret. Comput. Sci. 84(1), 127–150 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Berman, P.: On-line searching and navigation. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms. LNCS, vol. 1442, pp. 232–241. Springer, Heidelberg (1998). doi: 10.1007/BFb0029571 CrossRefGoogle Scholar
  4. 4.
    Xu, Y., Qin, L.: Strategies of groups evacuation from a convex region in the plane. In: Fellows, M., Tan, X., Zhu, B. (eds.) AAIM/FAW -2013. LNCS, vol. 7924, pp. 250–260. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38756-2_26 CrossRefGoogle Scholar
  5. 5.
    Wei, Q., Tan, X., Jiang, B., Wang, L.: On-line strategies for evacuating from a convex region in the plane. In: Zhang, Z., Wu, L., Xu, W., Du, D.-Z. (eds.) COCOA 2014. LNCS, vol. 8881, pp. 74–85. Springer, Cham (2014). doi: 10.1007/978-3-319-12691-3_7 Google Scholar
  6. 6.
    Wei, Q., Wang, L., Jiang, B.: Tactics for evacuating from an affected area. Int. J. Mach. Learn. Comput. 3(5), 435–439 (2013)CrossRefGoogle Scholar
  7. 7.
    Liu, Y., Jiang, B., Zhang, H.: Online strategies for evacuating from a convex region by groups in the plane. In: 2015 Ninth International Conference on Frontier of Computer Science and Technology, pp. 178–183. IEEE (2015)Google Scholar
  8. 8.
    Qin, L., Xu, Y.: Fibonacci helps to evacuate from a convex region in a grid network. J. Comb. Optim. 1–16 (2016)Google Scholar
  9. 9.
    Lu, Q., George, B., Shekhar, S.: Capacity constrained routing algorithms for evacuation planning: a summary of results. In: Bauzer Medeiros, C., Egenhofer, Max J., Bertino, E. (eds.) SSTD 2005. LNCS, vol. 3633, pp. 291–307. Springer, Heidelberg (2005). doi: 10.1007/11535331_17 CrossRefGoogle Scholar
  10. 10.
    Zhang, H., Xu, Y.: The k-Canadian travelers problem with communication. In: Atallah, M., Li, X.-Y., Zhu, B. (eds.) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. LNCS, vol. 6681, pp. 17–28. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-21204-8_6 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of ManagementXi’an Jiaotong UniversityXi’anChina
  2. 2.The State Key Lab for Manufacturing Systems EngineeringXi’anChina

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