Identifying Codes and Covering Problems

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Identifying Codes and Covering Problems
The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. Initially introduced in 1998, this problem has demonstrated its fundamental nature through a wide variety of applications, such as fault diagnosis, location detection, and environmental monitoring, in addition to deep connections to information theory, superimposed and covering codes, and tilings. This work establishes efficient reductions between the identifying code problem and the well-known setcovering problem, resulting in a tight hardness of approximation result and novel, provably tight polynomial-time approximations. The main results are also extended to r-robust identifying codes and analogous set (2r + 1)multicover problems. Finally, empirical support is provided for the effectiveness of the proposed approximations, including good constructions for well-known topologies such as infinite two-dimensional grids.
Moshe Laifenfeld, Ari Trachtenberg
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TIT
Authors Moshe Laifenfeld, Ari Trachtenberg
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