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Lower Bounds on Edge Searching

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Combinatorics, Algorithms, Probabilistic and Experimental Methodologies (ESCAPE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4614))

Abstract

Searching a network for intruders is an interesting and difficult problem. Edge-searching is one such search model, in which intruders may exist anywhere along an edge. Since finding the minimum number of searchers necessary to search a graph is NP–complete, it is natural to look for bounds on the search number. We show lower bounds on the search number using minimum degree, girth, chromatic number, and colouring number.

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References

  1. Alspach, B.: Searching and sweeping graphs: A brief survey. Combinatorics 04 (Catania, 2004) Matematiche (Catania) 59, Fasc. I–II, pp. 5–37 (2004)

    Google Scholar 

  2. Bienstock, D., Seymour, P.: Monotonicity in graph searching. Journal of Algorithms 12, 239–245 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fellows, M., Langston, M.: On search, decision and the efficiency of polynomial time algorithm. In: 21st ACM Symp. on Theory of Computing, pp. 501–512 (1989)

    Google Scholar 

  4. Frankling, M., Galil, Z., Yung, M.: Eavesdropping games: A graph-theoretic approach to privacy in distributed systems. Journal of ACM 47, 225–243 (2000)

    Article  Google Scholar 

  5. Halin, R.: Unterteilungen vollständiger Graphen in Graphen mit unendlicher chromatischer Zahl. Abh. Math. Sem. Univ. Hamburg 31, 156–165 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kirousis, L.M., Papadimitriou, C.H.: Searching and pebbling. Theoret. Comput. Sci. 47(2), 205–218 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  7. LaPaugh, A.S.: Recontamination does not help to search a graph. Journal of ACM 40, 224–245 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Megiddo, N., Hakimi, S.L., Garey, M., Johnson, D., Papadimitriou, C.H.: The complexity of searching a graph. Journal of ACM 35, 18–44 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mycielski, J.: Sur le coloriage des graphes. Coll. Math. 3, 161–162 (1955)

    MATH  MathSciNet  Google Scholar 

  10. Tusa, Z.: Exponentially many distinguishable cycles in graphs. Graphs, designs and combinatorial geometries (Catania, 1989). J. Combin. Inform. System Sci. 15, 281–285 (1990)

    MathSciNet  Google Scholar 

  11. Yang, B., Dyer, D., Alspach, B.: Sweeping graphs with large clique number (extended abstract). In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 880–892. Springer, Heidelberg (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Regina,  

    Brian Alspach & Denis Hanson

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland,  

    Danny Dyer

  3. Department of Computer Science, University of Regina,  

    Boting Yang

Authors
  1. Brian Alspach
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  2. Danny Dyer
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  3. Denis Hanson
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  4. Boting Yang
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Editor information

Bo Chen Mike Paterson Guochuan Zhang

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© 2007 Springer-Verlag Berlin Heidelberg

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Alspach, B., Dyer, D., Hanson, D., Yang, B. (2007). Lower Bounds on Edge Searching. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_46

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  • DOI: https://doi.org/10.1007/978-3-540-74450-4_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74449-8

  • Online ISBN: 978-3-540-74450-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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