The Covert Set-Cover Problem with Application to Network Discovery

  • Sandeep Sen
  • V. N. Muralidhara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)


We address a version of the set-cover problem where we do not know the sets initially (and hence referred to as covert) but we can query an element to find out which sets contain this element as well as query a set to know the elements. We want to find a small set-cover using a minimal number of such queries. We present a Monte Carlo randomized algorithm that approximates an optimal set-cover of size OPT within O(logN) factor with high probability using O( OPT ·log2 N ) queries where N is the number of elements in the universal set.

We apply this technique to the network discovery problem that involves certifying all the edges and non-edges of an unknown n-vertices graph based on layered-graph queries from a minimal number of vertices. By reducing it to the covert set-cover problem we present an O(log2 n)-competitive Monte Carlo randomized algorithm for the covert version of network discovery problem. The previously best known algorithm has a competitive ratio of \(\Omega ( \sqrt{n\log n} )\) and therefore our result achieves an exponential improvement.


Competitive Ratio Online Algorithm Competitive Algorithm Query Model Online Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., Naor, J.: The online set cover problem, pp. 100–105 (2003)Google Scholar
  2. 2.
    Awerbuch, B., Azar, Y., Fiat, A., Leighton, F.T.: Making commitments in the face of uncertainty: How to pick a winner almost every time (extended abstract), pp. 519–530 (1996)Google Scholar
  3. 3.
    Beerliova, Z., Eberhard, F., Erlebach, T., Hall, A., Hoffmann, M., Mihaľák, M., Shankar Ram, L.: Network discovery and verification. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 127–138. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Beerliova, Z., Eberhard, F., Erlebach, T., Hall, A., Hoffmann, M., Mihalák, M., Shankar Ram, L.: Network discovery and verification. IEEE Journal on Selected Areas in Communications 24(12), 2168–2181 (2006)CrossRefGoogle Scholar
  5. 5.
    Bejerano, Y., Rastogi, R.: Robust monitoring of link delays and faults in ip networks. In: INFOCOM (2003)Google Scholar
  6. 6.
    Jonson, D.S.: Approximation algorithms for combinatorial problem. Journal of Computer and System Sciences (9), 256–278 (1974)Google Scholar
  7. 7.
    Feige, U.: A threshold of ln for approximating set cover. J. ACM 45(4), 634–652 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Khuller, S., Raghavachari, B., Rosenfeld, A.: Landmarks in graphs. Discrete Applied Mathematics 70(3), 217–229 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Grey, M.R., Jonson, D.S.: Computers and intractability. Freeman, New York (1979)Google Scholar
  10. 10.
    Vazirani, V.V.: Approximation algorithms. Springer, New York (2001)Google Scholar
  11. 11.
    Chatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research (4), 233–235 (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sandeep Sen
    • 1
  • V. N. Muralidhara
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyDelhiIndia

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