Skip to main content

Search Games: A Review

  • Chapter
  • First Online:
Search Theory

Abstract

This review presents an update on the area of Search Games, highlighting recent developments in the field, as well as presenting some new problems for further research. The search space is either a graph, a bounded domain, a mixture of the above, or an unbounded set. The search process is presented as a two-player zero-sum game between the searcher and the hider. The searcher moves along a continuous trajectory and the cost function is the time needed to find the hider. Our review emphasises general results concerning minimax search trajectories and optimal search strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alpern, S. (1974). The search game with mobile hider on the circle. Pp. 181–200 in Roxin, EO, Liu, PT and Sternberg, RL, eds. Differential Games and Control Theory. Dekker, New York.

    Google Scholar 

  2. Alpern, S. (2008). Hide-and-seek games on a tree to which Eulerian networks are attached. Networks 52(3):109–178.

    Article  MathSciNet  Google Scholar 

  3. Alpern, S. and Gal, S. (1988). A mixed strategy minimax theorem without compactness. SIAM J. Control Optim. 26:1357–1361.

    Article  MathSciNet  MATH  Google Scholar 

  4. Alpern, S. and Gal, S. (2003). The theory of search games and rendezvous. Springer.

    Google Scholar 

  5. Alpern, S., Baston, V, and Gal, S. (2008). Network search games with immobile hider, without a designated searcher starting point. International Journal of Game Theory 37:281–302.

    Article  MathSciNet  MATH  Google Scholar 

  6. Alpern, S., Fokkink, R., Lindelauf, R. and Olsder, GJ. (2008). The Princess and Monster game on an interval. SIAM Journal on Control and Optimization. (47):1178–1190.

    Google Scholar 

  7. Anderson, EJ. and Aramendia, MA. (1990). The search game on a network with immobile hider. Networks. 20(7):817–844.

    Article  MathSciNet  MATH  Google Scholar 

  8. Baeza-Yates, R. A., Culberson, J. C. and Rawlins, G. J. E. (1993). Searching in the plane. Inf. Comput. 106(2):234–252.

    Article  MathSciNet  MATH  Google Scholar 

  9. Bellman, R. (1956). Minimization problem. Bull. Am. Math. Soc. 62:270.

    Article  Google Scholar 

  10. Bellman, R. (1963). An optimal search problem. SIAM Rev. 5:274.

    Article  Google Scholar 

  11. Beck, A. (1964). On the linear search Problem. Israel J. Mathematics. 2:221–228.

    Article  MATH  Google Scholar 

  12. Beck, A. (1965). More on the linear search problem. Israel J. Mathematics. 3:61–70.

    Article  Google Scholar 

  13. Beck, A. and Beck, M. (1986). The linear search problem rides again. Israel J. Mathematics. 53(3):365–372.

    Article  MATH  Google Scholar 

  14. Beck, A. and Newman, DJ. (1970). Yet More on the linear search problem. Israel J. Mathematics. 8:419–429.

    Article  MathSciNet  MATH  Google Scholar 

  15. Borodin A. and El-Yaniv, R. (1998). Online Computation and Competitive Analysis. Cambridge University Press.

    Google Scholar 

  16. Bruce, TF. and Robertson, JB. (1988). A survey of the linear-search problem. Math. Sci. 13: 75–89.

    MathSciNet  Google Scholar 

  17. Chrobak M. and Kenyon-Mathieu, C. (2006). Competitiveness via doubling. SIGACT News. 37(4):115–126.

    Article  Google Scholar 

  18. Dagan, A. and Gal, S. (2008). Network search games, with arbitrary searcher starting point. Networks. 52(3):156–161.

    Article  MathSciNet  MATH  Google Scholar 

  19. Demaine, ED., Fekete, S. and Gal, S. (2006). Online searching with turn cost. Theoretical Computer Science. 361:342–355.

    Article  MathSciNet  MATH  Google Scholar 

  20. Even, S. (1979). Graph Algorithms. Computer Science Press, Rockville MD. Ch. 3.

    Google Scholar 

  21. Edmonds, J, and Johnson, EL. (1973). Matching Euler tours and the Chinese postman problem. Math. Program. 5:88–124.

    Article  MathSciNet  MATH  Google Scholar 

  22. Gal, S. (1974). Minimax solutions for linear search problems. SIAM J. Appl. Math. 27:17–30.

    Article  MathSciNet  MATH  Google Scholar 

  23. Gal, S. (1979). Search games with mobile and immobile hider. SIAM J. Control Optim. 17: 99–122.

    Article  MathSciNet  MATH  Google Scholar 

  24. Gal, S. (1980). Search Games. Academic Press, New York.

    MATH  Google Scholar 

  25. Gal, S. (2000). On the optimality of a simple strategy for searching graphs. Int. J. Game Theory. 29:533–542.

    Article  MathSciNet  Google Scholar 

  26. Gal, S. (2011). Search Games. Wiley Encyclopedia of Operations Research and Management Science.

    Google Scholar 

  27. Gal, S. and Anderson, EJ. (1990). Search in a maze. Probab. Eng. Inf. Sci. (4):311–318.

    Google Scholar 

  28. Gal, S and Chazan, D. (1976). On the optimality of the exponential functions for some minimax problems. SIAM J. Appl. Math. 1976.30:324–348.

    Google Scholar 

  29. Garnaev, A. (1992). A Remark on the Princess and Monster Search Game. Int. J. of Game Theory. 20:269–276.

    Article  MathSciNet  MATH  Google Scholar 

  30. Isaacs, R. (1965). Differential Games. Wiley, New York.

    MATH  Google Scholar 

  31. Isbell, J. R. (1957). An optimal search pattern. Naval Res. Logist. Quart. (4):357–359.

    Google Scholar 

  32. Kao, M, Reif, JH, Tate, SR. (1996). Searching an unknown envitonment: an optimal randomized algorithm for the cow-path problem. Inf. Comput. 131(1):63–79.

    Article  MathSciNet  MATH  Google Scholar 

  33. Kao, MY., Ma Y., Sipser, M. and Yin, Y. (1998). Optimal construction of Hybrid algorithm. J. of Algorithms. 29:142–164.

    Article  MathSciNet  MATH  Google Scholar 

  34. Kella, O. (1993). Star search – a different show. Israel. J. Mathematics. 81:145–159.

    Article  MathSciNet  MATH  Google Scholar 

  35. Lalley, SP. and Robbins, HE. (1988). Stochastic search in a convex region. Probab. Theory Relat. Fields. 77(1):99–116.

    Article  MathSciNet  MATH  Google Scholar 

  36. Langetepe, E. (2009). On the Optimality of Spiral Search. SODA 2010.

    Google Scholar 

  37. López-Ortiz, A. and Schuierer, S. (2001). The ultimate strategy to search on m rays? Theoretical Computer Science. 261(2):267–295.

    Article  MathSciNet  MATH  Google Scholar 

  38. López-Ortiz, A. and Schuierer, S. (2004). Online parallel heuristics, processor scheduling, and robot searching under the competitive framework. Theoretical Computer Science. 310: 527–537.

    Article  MathSciNet  MATH  Google Scholar 

  39. Lucas, E. (1882). Recreations Mathematique. Paris

    Google Scholar 

  40. Pavlovic, L. (1993). Search game on an odd number of arcs with immobile hider. Yugosl. J. Oper. Res. 3(1):11–19.

    MathSciNet  MATH  Google Scholar 

  41. Schuierer, S. (2003). A lower Bound for Randomized Searching on m Rays, Pp 264–277 in Klein, R, Six, HW and Wegner, L. eds, Computer Science in Perspective: Essays Dedicated to Thomas Ottmann, volume 2598 of Lecture Notes Comput. Sci. Springer-Verlag, Berlin.

    Google Scholar 

  42. Tarry, G. (1985). La problem des labyrinths. Nouvelles Annals de Mathematique. 14, 187.

    Google Scholar 

  43. Von Stengel, B. and Werchner, R. (1997). Complexity of searching an immobile hider in a graph. Discrete Appl. Math. 78:235–249.

    Article  MathSciNet  MATH  Google Scholar 

  44. Wilson, DJ. (1970). Isaacs’ princess and monster game on the circle. JOTA. 9:265–288.

    Article  Google Scholar 

  45. Zelikin, MI. (1972). On a differential game with incomplete information. Soviet Math. Dokl. 13:228–231.

    Google Scholar 

Download references

Acknowledgements

The author would like to thank the Lorentz Center, the organizing committee of the workshop on Search and Rendezvous, and especially Robbert Fokkink and Steve Alpern for their help and support. The author is also obliged to Robbert Fokkink for his useful remarks which led to a significantly improved version.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shmuel Gal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Gal, S. (2013). Search Games: A Review. In: Alpern, S., Fokkink, R., GÄ…sieniec, L., Lindelauf, R., Subrahmanian, V. (eds) Search Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6825-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-6825-7_1

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6824-0

  • Online ISBN: 978-1-4614-6825-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics