The minimum density of an identifying code in the king lattice

Charon, Irène; Honkala, Iiro; Hudry, Olivier; Lobstein, Antoine

doi:10.1016/s0012-365x(03)00306-6

Cited by 43 publications

(41 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, 2 k+1 }}. Then the code C = C 1 ∪ C 2 has density 3 8 . In the diagonal pattern S r,∆ ((0, 0), (−1, −1)) there are at least the four vertices (a, b), (b, a), (a, b − 1), (b − 1, a) and their symmetric images by a central rotation in (−0.5, −0.5).…”

Section: Claim (Ii)mentioning

confidence: 99%

See 1 more Smart Citation

Tolerant identification with Euclidean balls

2012

View full text Add to dashboard Cite

The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. The identifying codes can be applied, for example, to sensor networks. In this paper, we consider as sensors the set Z 2 where one sensor can check its neighbours within Euclidean distance r. We construct tolerant identifying codes in this network that are robust against some changes in the neighbourhood monitored by each sensor. We give bounds for the smallest density of a tolerant identifying code for general values of r. We also provide infinite families of values r with optimal such codes and study the case of small values of r.

show abstract

Section: Claim (Ii)mentioning

confidence: 99%

“…For special values of r, this graph has been considered in many papers, for example, [1,3,6,8,9]. For related results, see [2,12].…”

Section: Introductionmentioning

confidence: 99%

Tolerant identification with Euclidean balls

2012

View full text Add to dashboard Cite

show abstract

“…7) While C is not empty, 8) Update dist(C, C j ) and path(C, C j ) for every C j ∈ C and set C * ← arg min Cj ∈ b C dist(C, C j ).…”

Section: Iterationmentioning

confidence: 99%

“…Although introduced only twelve years ago [1], identifying codes have been linked to a number of deeply researched theoretical foundations, including super-imposed codes [2], covering codes [1,3], locating-dominating sets [4], and tilings [5][6][7][8]. They have also been generalized and used for detecting faults or failures in multi-processor systems [1], RF-based localization in harsh environments [9][10][11], and routing in networks [12].…”

Section: Introductionmentioning

confidence: 99%

Connecting identifying codes and fundamental bounds

Fazlollahi

Starobinski

Trachtenberg

2011

2011 Information Theory and Applications Workshop

View full text Add to dashboard Cite

Abstract-We consider the problem of generating a connected robust identifying code of a graph, by which we mean a subgraph with two properties: (i) it is connected, (ii) it is robust identifying, in the sense that the (subgraph-) induced neighborhoods of any two vertices differ by at least 2r + 1 vertices, where r is the robustness parameter. This particular formulation builds upon a rich literature on the identifying code problem but adds a property that is important for some practical networking applications. We concretely show that this modified problem is NP-complete and provide an otherwise efficient algorithm for computing it for an arbitrary graph. We demonstrate a connection between the the sizes of certain connected identifying codes and errorcorrecting code of a given distance. One consequence of this is that robustness leads to connectivity of identifying codes.

show abstract

“…Significant efforts in the research of identifying codes and their variants have focused on finding efficient constructions in two dimensional lattices, grids and Hamming spaces (see [12,[23][24][25][26], and [6] for a summary of recent results). Until recently, little has been published towards a polynomial time approximation algorithm for arbitrary graphs.…”

Section: Introductionmentioning

confidence: 99%

Identifying Codes and Covering Problems

Laifenfeld

Trachtenberg²

2008

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

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. Index TermsIdentifying codes, robust identifying codes, hardness of approximation, set cover, test cover, distributed algorithms.

show abstract

The minimum density of an identifying code in the king lattice

Cited by 43 publications

References 10 publications

Tolerant identification with Euclidean balls

Tolerant identification with Euclidean balls

Connecting identifying codes and fundamental bounds

Identifying Codes and Covering Problems

Contact Info

Product

Resources

About