On the Fast Searching Problem

  • Danny Dyer
  • Boting Yang
  • Öznur Yaşar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)


Edge searching is a graph problem that corresponds to cleaning a contaminated graph using the minimum number of searchers. We define fast searching as a variant of this widely studied problem. Fast searching corresponds to an internal monotone search in which every edge is traversed exactly once and searchers are not allowed to jump. We present a linear time algorithm to compute the fast search number of trees. We investigate the fast search number of bipartite graphs. We also propose a general cost function for evaluating search strategies that utilizes both edge searching and fast searching.


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  1. 1.
    Alspach, B., Dyer, D., Hanson, D., Yang, B.: Lower bounds on edge searching. In: Chen, B., Paterson, M., Zhang, G. (eds.) ESCAPE 2007. LNCS, vol. 4614, pp. 516–527. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Capture of an intruder by mobile agents. In: Proceedings of the 14th annual ACM symposium on Parallel algorithms and architectures (SPAA 2002), pp. 200–209 (2002)Google Scholar
  3. 3.
    Barrière, L., Fraigniaud, P., Santoro, N., Thilikos, D.: Searching is not Jumping. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 34–45. Springer, Heidelberg (2003)Google Scholar
  4. 4.
    Bienstock, D., Seymour, P.: Monotonicity in Graph Searching. Journal of Algorithms 12, 239–245 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Breisch, R.L.: An intuitive approach to speleotopology. Southwestern Cavers 6, 72–78 (1967)Google Scholar
  6. 6.
    Chung, F.: On the cutwidth and the topological bandwidth of a tree. SIAM J. Algebraic Discrete Methods 6, 268–277 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Fomin, F.V., Golovach, P.A.: Interval completion and graph searching. SIAM Journal on Discrete Mathematics 13, 454–464 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theoretical Computer Science, Special Issue on Graph Searching (submitted on November 2007)Google Scholar
  9. 9.
    Kinnersley, N.G.: The Vertex Separation Number of a graph equals its path-width. Information Processing Letters 42, 345–350 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    LaPaugh, A.S.: Recontamination does not help to search a graph. Journal of ACM 40, 224–245 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Megiddo, N., Hakimi, S.L., Garey, M.R., Johnson, D.S., Papadimitriou, C.H.: The Complexity of Searching a Graph. Journal of ACM 35, 18–44 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Parsons, T.: Pursuit-evasion in a graph. In: Theory and Applications of Graphs. Lecture Notes in Mathematics, pp. 426–441. Springer, Heidelberg (1976)Google Scholar
  13. 13.
    West, D.B.: Introduction to Graph Theory. Prentice Hall, Englewood Cliffs (1996)zbMATHGoogle Scholar
  14. 14.
    Yang, B., Dyer, D., Alspach, B.: Sweeping graphs with large clique number. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 908–920. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Danny Dyer
    • 1
  • Boting Yang
    • 2
  • Öznur Yaşar
    • 1
  1. 1.Department of Mathematics and StatisticsMemorial University of Newfoundland 
  2. 2.Department of Computer ScienceUniversity of Regina 

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