Autonomous Robots

, Volume 29, Issue 1, pp 99–118 | Cite as

GSST: anytime guaranteed search

  • Geoffrey HollingerEmail author
  • Athanasios Kehagias
  • Sanjiv Singh


We present Guaranteed Search with Spanning Trees (GSST), an anytime algorithm for multi-robot search. The problem is as follows: clear the environment of any adversarial target using the fewest number of searchers. This problem is NP-hard on arbitrary graphs but can be solved in linear-time on trees. Our algorithm generates spanning trees of a graphical representation of the environment to guide the search. At any time, spanning tree generation can be stopped yielding the best strategy so far. The resulting strategy can be modified online if additional information becomes available. Though GSST does not have performance guarantees after its first iteration, we prove that several variations will find an optimal solution given sufficient runtime. We test GSST in simulation and on a human-robot search team using a distributed implementation. GSST quickly generates clearing schedules with as few as 50% of the searchers used by competing algorithms.


Multi-robot coordination Graph search Anytime algorithms Decentralized computation Pursuit/evasion 


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  1. Alspach, B. (2006). Searching and sweeping graphs: a brief survey. Matematiche, 59, 5–37. MathSciNetGoogle Scholar
  2. Barrière, L., Flocchini, P., Fraigniaud, P., & Santoro, N. (2002). Capture of an intruder by mobile agents. In Proc. 14th ACM symp. parallel algorithms and architectures (pp. 200–209). Google Scholar
  3. Barrière, L., Fraigniaud, P., Santoro, N., & Thilikos, D. (2003). Searching is not jumping. Graph-Theoretic Concepts in Computer Science, 2880, 34–45. Google Scholar
  4. Bienstock, D., & Seymour, P. (1991). Monotonicity in graph searching. Journal of Algorithms, 12(2), 239–245. zbMATHCrossRefMathSciNetGoogle Scholar
  5. Char, J. (1968). Generation of trees, two-trees, and storage of master forests. IEEE Transactions on Circuit Theory, 15(3), 228–238. CrossRefMathSciNetGoogle Scholar
  6. Dendris, N., Kirousis, L., & Thilikos, D. (1994). Fugitive-search games on graphs and related parameters. In Proc. 20th int. workshop graph-theoretic concepts in computer science (pp. 331–342). Google Scholar
  7. Flocchini, P., Nayak, A., & Schulz, A. (2005). Cleaning an arbitrary regular network with mobile agents. In Proc. int. conf. distributed computing and Internet technology (pp. 132–142). Google Scholar
  8. Flocchini, P., Huang, M., & Luccio, F. (2007). Decontamination of chordal rings and tori using mobile agents. International Journal of Foundations of Computer Science, 18(3), 547–564. zbMATHCrossRefMathSciNetGoogle Scholar
  9. Flocchini, P., Huang, M., & Luccio, F. (2008). Decontamination of hypercubes by mobile agents. Networks, 52(3), 167–178. zbMATHCrossRefMathSciNetGoogle Scholar
  10. Fomin, F., & Thilikos, D. (2008). An annotated bibliography on guaranteed graph searching. Theoretical Computer Science, 399, 236–245. zbMATHCrossRefMathSciNetGoogle Scholar
  11. Fomin, F., Fraigniaud, P., & Thilikos, D. (2004). The price of connectedness in expansions. Technical Report LSI-04-28-R, UPC Barcelona. Google Scholar
  12. Fraigniaud, P., & Nisse, N. (2006). Connected treewidth and connected graph searching. In Proc. 7th Latin American symp. theoretical informatics. Google Scholar
  13. Gerkey, B. (2004). Pursuit-evasion with teams of robots.
  14. Gerkey, B., Vaughan, R., & Howard, A. (2003). The player/stage project: tools for multi-robot and distributed sensor systems. In Proc. int. conf. advanced robotics (pp. 317–323). Google Scholar
  15. Gerkey, B., Thrun, S., & Gordon, G. (2005). Parallel stochastic hill-climbing with small teams. In Proc. 3rd int. NRL workshop multi-robot systems. Google Scholar
  16. Guibas, L., Latombe, J., LaValle, S., Lin, D., & Motwani, R. (1999). Visibility-based pursuit-evasion in a polygonal environment. International Journal of Computational Geometry and Applications, 9(5), 471–494. CrossRefMathSciNetGoogle Scholar
  17. Hollinger, G., Kehagias, A., & Singh, S. (2009a). Efficient, guaranteed search with multi-agent teams. In Proc. robotics: science and systems conf. Google Scholar
  18. Hollinger, G., Singh, S., Djugash, J., & Kehagias, A. (2009b). Efficient multi-robot search for a moving target. International Journal of Robotics Research, 28(2), 201–219. CrossRefGoogle Scholar
  19. Isler, V., Kannan, S., & Khanna, S. (2005). Randomized pursuit-evasion in a polygonal environment. IEEE Transactions on Robotics, 21(5), 875–884. CrossRefGoogle Scholar
  20. Kalra, N. (2006). A market-based framework for tightly-coupled planned coordination in multirobot teams. Ph.D. thesis, Robotics Institute, Carnegie Mellon Univ. Google Scholar
  21. Kehagias, A., Hollinger, G., & Gelastopoulos, A. (2009a). Searching the nodes of a graph: theory and algorithms. Technical Report arXiv:0905.3359 [cs.DM].
  22. Kehagias, A., Hollinger, G., & Singh, S. (2009b). A graph search algorithm for indoor pursuit/evasion. Mathematical and Computer Modelling, 50(9–10), 1305–1317. zbMATHCrossRefMathSciNetGoogle Scholar
  23. Kloks, T. (1994). Treewidth: computations and approximations. Berlin: Springer. zbMATHGoogle Scholar
  24. Kolling, A., & Carpin, S. (2008). Extracting surveillance graphs from robot maps. In Proc. int. conf. intelligent robots and systems. Google Scholar
  25. Kolling, A., & Carpin, S. (2010). Pursuit-evasion on trees by robot teams. IEEE Transactions on Robotics, 26, 32–47. CrossRefGoogle Scholar
  26. Kumar, V., Rus, D., & Singh, S. (2004). Robot and sensor networks for first responders. Pervasive Computing, 3(4), 24–33. CrossRefGoogle Scholar
  27. LaPaugh, A. (1993). Recontamination does not help to search a graph. Journal of ACM, 40(2), 224–245. zbMATHCrossRefMathSciNetGoogle Scholar
  28. LaValle, S. M. (2006). Planning algorithms. Cambridge: Cambridge University Press. zbMATHCrossRefGoogle Scholar
  29. LaValle, S., Lin, D., Guibas, L., Latombe, J., & Motwani, R. (1997). Finding an unpredictable target in a workspace with obstacles. In Proc. IEEE international conf. robotics and automation. Google Scholar
  30. Likhachev, M., Ferguson, D., Gordon, G., Stentz, A., & Thrun, S. (2005). Anytime dynamic A*: an anytime, replanning algorithm. In Proc. int. conf. automated planning and scheduling. Google Scholar
  31. Megiddo, N., Hakimi, S., Garey, M., Johnson, D., & Papadimitriou, C. (1988). The complexity of searching a graph. Journal of ACM, 35(1), 18–44. zbMATHCrossRefMathSciNetGoogle Scholar
  32. Parsons, T. (1976). Pursuit-evasion in a graph. In Y. Alavi, & D. Lick (Eds.) Theory and applications of graphs (pp. 426–441). Berlin: Springer. Google Scholar
  33. Shewchuk, J. (2002). Delaunay refinement algorithms for triangular mesh generation. Computational Geometry: Theory and Applications, 22(1–3), 21–74. zbMATHMathSciNetGoogle Scholar
  34. Smith, T. (2007). Probabilistic planning for robotic exploration. Ph.D. thesis, Robotics Institute, Carnegie Mellon Univ. Google Scholar
  35. Wilson, D. (1996). Generating random spanning trees more quickly than the cover time. In Proc. 28th ACM symp. theory of computing (pp. 296–303). Google Scholar
  36. Yang, B., Dyer, D., & Alspach, B. (2004). Sweeping graphs with large clique number. In Proc. 5th international symp. algorithms and computation (pp. 908–920). Google Scholar
  37. Zilberstein, S. (1996). Using anytime algorithms in intelligent systems. Artificial Intelligence Magazine, 17(3), 73–86. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Geoffrey Hollinger
    • 1
    Email author
  • Athanasios Kehagias
    • 2
  • Sanjiv Singh
    • 1
  1. 1.Robotics InstituteCarnegie Mellon UniversityPittsburghUSA
  2. 2.Faculty of EngineeringAristotle University of ThessalonikiThessalonikiGreece

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