The d-Identifying Codes Problem for Vertex Identification in Graphs: Probabilistic Analysis and an Approximation Algorithm

  • Ying Xiao
  • Christoforos Hadjicostis
  • Krishnaiyan Thulasiraman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


Given a graph G(V, E), the identifying codes problem is to find the smallest set of vertices D ⊆ V such that no two vertices in V are adjacent to the same set of vertices in D. The identifying codes problem has been applied to fault diagnosis and sensor based location detection in harsh environments. In this paper, we introduce and study a generalization of this problem, namely, the d-identifying codes problem. We propose a polynomial time approximation algorithm based on ideas from information theory and establish its approximation ratio that is very close to the best possible. Using analysis on random graphs, several fundamental properties of the optimal solution to this problem are also derived.


Equivalence Class Approximation Algorithm Greedy Algorithm Random Graph Approximation Ratio 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ying Xiao
    • 1
  • Christoforos Hadjicostis
    • 2
  • Krishnaiyan Thulasiraman
    • 3
  1. 1.Packet Design Inc.Palo AltoUSA
  2. 2.University of Illinois at Urbana-ChampaignUSA
  3. 3.University of OklahomaNormanUSA

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