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Online graph exploration algorithms for cycles and trees by multiple searchers

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Abstract

This paper deals with online graph exploration problems by multiple searchers. The information on the graph is given online. As the exploration proceeds, searchers gain more information on the graph. Assuming an appropriate communication model among searchers, searchers can share the information about the environment. Thus, a searcher must decide which vertex to visit next based on the partial information on the graph gained so far by searchers. We assume that all searchers initially start the exploration at the origin vertex, and the goal is that each vertex is visited by at least one searcher and all searchers finally return to the origin vertex. The objective is to minimize the time when the goal is achieved. We study the case of cycles and trees. For the former, we give an optimal online exploration algorithm in terms of competitive ratio, and for the latter, we also give an online exploration algorithm which is optimal among greedy algorithms.

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References

  • Albers S, Henzinger MR (2000) Exploring unknown environments. SIAM J Comput 29(4):1164–1188

    Article  MATH  MathSciNet  Google Scholar 

  • Ausiello G, Feuerstein E, Leonardi S, Stougie L, Talamo M (2001) Algorithms for the on-line travelling salesman. Algorithmica 130:560–581

    Article  MathSciNet  Google Scholar 

  • Ausiello G, Demange M, Laura L, Paschos V (2004) Algorithms for the on-line quota traveling salesman problem. Inf Process Lett 92(2):89–94

    Article  MATH  MathSciNet  Google Scholar 

  • Averbakh I, Berman O (1997) \((p-1)/(p+ 1)\)-approximate algorithms for \(p\)-traveling salesmen problems on a tree with minmax objective. Discr Appl Math 75(3):201–216

    Article  MATH  MathSciNet  Google Scholar 

  • Blom M, Krumke SO, de Paepe WE, Stougie L (2001) The online TSP against fair adversaries. INFORMS J Comput 13(2):138–148

    Article  MATH  MathSciNet  Google Scholar 

  • Brass P, Gasparri A, Cabrera-Mora F, Xiao J (2009) Multi-robot tree and graph exploration. IEEE Trans Robotics 27(4):707–717

    Article  Google Scholar 

  • Deng X, Papadimitriou CH (1999) Exploring an unknown graph. J Graph Theory 32(3):265–297

    Article  MATH  MathSciNet  Google Scholar 

  • Dobrev S, Královic R, Markou E (2012) Online graph exploration with advice. In: Proceedings of SIROCCO 2012. LNCS, vol 7355, pp 267–278

  • Duncan CA, Kobourov SG, Kumar VSA (2006) Optimal constrained graph exploration. ACM Trans Algorithms 2(3):380–402

    Article  MathSciNet  Google Scholar 

  • Dynia M, Korzeniowski M, Schindelhauer C (2006) Power-aware collective tree exploration. In: Proceedings of ARCS 2006. LNCS, vol 3894, pp 341–351

  • Dynia M, Kutylowski J, Meyer auf der Heide F, Schindelhauer C (2006) Smart robot teams exploring sparse trees. In: Proceedings of MFCS 2006. LNCS, vol 4162, pp 327–338

  • Dynia M, Lopuszanski J, Schindelhauer C (2007) Why robots need maps. In: Proceedings of SIROCCO 2007. LNCS, vol 4474, pp 41–50

  • Fleischer R, Trippen G (2005) Exploring an unknown graph efficiently. In: Proceedings of 13th ESA. LNCS, vol 3669, pp 11–22

  • Fleischer R, Kamphans T, Klein R, Langetepe E, Trippen G (2008) Competitive online approximation of the optimal search ratio. SIAM J Comput 38(3):881–898

    Article  MATH  MathSciNet  Google Scholar 

  • Fraigniaud P, Gsieniec L, Kowalski DR, Pelc A (2006) Collective tree exploration. Networks 48(3):166–177

    Article  MATH  MathSciNet  Google Scholar 

  • Hoffmann F, Icking C, Klein R, Kriegel K (2002) The polygon exploration problem. SIAM J Comput 31(2):577–600

    Article  MathSciNet  Google Scholar 

  • Kalyanasundaram B, Pruhs KR (1994) Constructing competitive tours from local information. Theor Comput Sci 130:125–138

    Article  MATH  MathSciNet  Google Scholar 

  • Megow N, Mehlhorn K, Schweitzer P (2011) Online graph exploration: new results on old and new aldorithms. In: Proceedings of 38th ICALP. LNCS, vol 6756, pp 478–489

  • Miyazaki S, Morimoto N, Okabe Y (2009) The online graph exploration problem on restricted graphs. IEICE Trans Inf Syst E92-D(9):1620–1627

  • Nagamochi H, Okada K (2007) Approximating the minmax rooted-tree cover in a tree. Inf Process Lett 104:173–175

    Article  MATH  MathSciNet  Google Scholar 

  • Panaite P, Pelc A (1999) Exploring unknown undirected graphs. J Algorithms 33(2):281–295

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The second author is supported by JSPS Grant-in-Aid for Scientific Research(B) (21300003). The fourth author is supported by Grant-in-Aid for JSPS Research Fellowships for Young Scientists.

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Authors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo-ku, Kyoto, 615-8540, Japan

    Yuya Higashikawa & Naoki Katoh

  2. Département d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Stefan Langerman

  3. Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

    Shin-ichi Tanigawa

Authors
  1. Yuya Higashikawa
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  2. Naoki Katoh
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  3. Stefan Langerman
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  4. Shin-ichi Tanigawa
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Correspondence to Yuya Higashikawa.

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Higashikawa, Y., Katoh, N., Langerman, S. et al. Online graph exploration algorithms for cycles and trees by multiple searchers . J Comb Optim 28, 480–495 (2014). https://doi.org/10.1007/s10878-012-9571-y

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  • DOI: https://doi.org/10.1007/s10878-012-9571-y

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