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.
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References
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.
Alpern, S. (2008). Hide-and-seek games on a tree to which Eulerian networks are attached. Networks 52(3):109–178.
Alpern, S. and Gal, S. (1988). A mixed strategy minimax theorem without compactness. SIAM J. Control Optim. 26:1357–1361.
Alpern, S. and Gal, S. (2003). The theory of search games and rendezvous. Springer.
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.
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.
Anderson, EJ. and Aramendia, MA. (1990). The search game on a network with immobile hider. Networks. 20(7):817–844.
Baeza-Yates, R. A., Culberson, J. C. and Rawlins, G. J. E. (1993). Searching in the plane. Inf. Comput. 106(2):234–252.
Bellman, R. (1956). Minimization problem. Bull. Am. Math. Soc. 62:270.
Bellman, R. (1963). An optimal search problem. SIAM Rev. 5:274.
Beck, A. (1964). On the linear search Problem. Israel J. Mathematics. 2:221–228.
Beck, A. (1965). More on the linear search problem. Israel J. Mathematics. 3:61–70.
Beck, A. and Beck, M. (1986). The linear search problem rides again. Israel J. Mathematics. 53(3):365–372.
Beck, A. and Newman, DJ. (1970). Yet More on the linear search problem. Israel J. Mathematics. 8:419–429.
Borodin A. and El-Yaniv, R. (1998). Online Computation and Competitive Analysis. Cambridge University Press.
Bruce, TF. and Robertson, JB. (1988). A survey of the linear-search problem. Math. Sci. 13: 75–89.
Chrobak M. and Kenyon-Mathieu, C. (2006). Competitiveness via doubling. SIGACT News. 37(4):115–126.
Dagan, A. and Gal, S. (2008). Network search games, with arbitrary searcher starting point. Networks. 52(3):156–161.
Demaine, ED., Fekete, S. and Gal, S. (2006). Online searching with turn cost. Theoretical Computer Science. 361:342–355.
Even, S. (1979). Graph Algorithms. Computer Science Press, Rockville MD. Ch. 3.
Edmonds, J, and Johnson, EL. (1973). Matching Euler tours and the Chinese postman problem. Math. Program. 5:88–124.
Gal, S. (1974). Minimax solutions for linear search problems. SIAM J. Appl. Math. 27:17–30.
Gal, S. (1979). Search games with mobile and immobile hider. SIAM J. Control Optim. 17: 99–122.
Gal, S. (1980). Search Games. Academic Press, New York.
Gal, S. (2000). On the optimality of a simple strategy for searching graphs. Int. J. Game Theory. 29:533–542.
Gal, S. (2011). Search Games. Wiley Encyclopedia of Operations Research and Management Science.
Gal, S. and Anderson, EJ. (1990). Search in a maze. Probab. Eng. Inf. Sci. (4):311–318.
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.
Garnaev, A. (1992). A Remark on the Princess and Monster Search Game. Int. J. of Game Theory. 20:269–276.
Isaacs, R. (1965). Differential Games. Wiley, New York.
Isbell, J. R. (1957). An optimal search pattern. Naval Res. Logist. Quart. (4):357–359.
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.
Kao, MY., Ma Y., Sipser, M. and Yin, Y. (1998). Optimal construction of Hybrid algorithm. J. of Algorithms. 29:142–164.
Kella, O. (1993). Star search – a different show. Israel. J. Mathematics. 81:145–159.
Lalley, SP. and Robbins, HE. (1988). Stochastic search in a convex region. Probab. Theory Relat. Fields. 77(1):99–116.
Langetepe, E. (2009). On the Optimality of Spiral Search. SODA 2010.
López-Ortiz, A. and Schuierer, S. (2001). The ultimate strategy to search on m rays? Theoretical Computer Science. 261(2):267–295.
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.
Lucas, E. (1882). Recreations Mathematique. Paris
Pavlovic, L. (1993). Search game on an odd number of arcs with immobile hider. Yugosl. J. Oper. Res. 3(1):11–19.
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.
Tarry, G. (1985). La problem des labyrinths. Nouvelles Annals de Mathematique. 14, 187.
Von Stengel, B. and Werchner, R. (1997). Complexity of searching an immobile hider in a graph. Discrete Appl. Math. 78:235–249.
Wilson, DJ. (1970). Isaacs’ princess and monster game on the circle. JOTA. 9:265–288.
Zelikin, MI. (1972). On a differential game with incomplete information. Soviet Math. Dokl. 13:228–231.
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.
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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
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