Identifying Codes and Covering Problems

Laifenfeld, Moshe; Trachtenberg, Ari

doi:10.1109/tit.2008.928263

Cited by 42 publications

(33 citation statements)

References 41 publications

(89 reference statements)

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“…The same properties hold for Min Test Cover [24] (and by Proposition 4, using Reduction 2 this result transfers to Min Discriminating Code) and Min Id Code (see [6,43,56], for different proofs). Min Discriminating Code was shown to be NP-hard, even when the bipartite incidence graph of the input hypergraph is planar [13].…”

Section: Related Workmentioning

confidence: 63%

“…We refer to [45] for an on-line bibliography on these topics, which lists more than 240 papers as of February 2013. In particular, see [2,3,6,17,28,30,31,34,43,49,54,55,56] for studies of the computational complexity of these problems. We remark that in many of these papers, due to the similarity between the two problems, the algorithmic properties of identifying codes and locating-dominating sets are studied together.…”

Section: Definitions and Problemsmentioning

confidence: 99%

“…This result holds even for bipartite graphs [17], and for Id Code it holds for planar graphs of maximum degree 3 [2,3], planar bipartite unit disk graphs [49], line graphs [30], split graphs [28,31], and, interestingly, interval graphs [28,31]. Regarding the minimization problems, log-APX-completeness of Min Id Code and Min Loc-Dom Set is known only for general graphs [6,43,56], and the two problems are APX-complete for graphs of bounded maximum degree at least 8 and 5, respectively [34].…”

Section: Related Workmentioning

confidence: 99%

“…Prior, three different papers [6,43,56] showed that Min Id Code is log-APX-complete, but only in general graphs. Moreover, the proofs of [6,43,56] are relatively involved, while we use the intuitive proximity between Min Discriminating Code and Min Id Code to design much simpler reductions. Note that on co-bipartite graphs, Min Dominating Set is in fact trivially solvable in polynomial time; in contrast, our result shows that Min Id Code and Min Loc-Dom Set are computationally very hard on this class.…”

Section: Min Id Codementioning

confidence: 99%

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Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes

Foucaud

2015

Journal of Discrete Algorithms

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An identifying code is a subset of vertices of a graph with the property that each vertex is uniquely determined (identified) by its nonempty neighbourhood within the identifying code. When only vertices out of the code are asked to be identified, we get the related concept of a locating-dominating set. These notions are closely related to a number of similar and well-studied concepts such as the one of a test cover. In this paper, we study the decision problems Identifying Code and Locating-Dominating Set (which consist in deciding whether a given graph admits an identifying code or a locating-dominating set, respectively, with a given size) and their minimization variants Minimum Identifying Code and Minimum LocatingDominating Set. These problems are known to be NP-hard, even when the input graph belongs to a number of specific graph classes such as planar bipartite graphs. Moreover, it is known that they are approximable within a logarithmic factor, but hard to approximate within any sub-logarithmic factor. We extend the latter result to the case where the input graph is bipartite, split or co-bipartite: both problems remain hard in these cases. Among other results, we also show that for bipartite graphs of bounded maximum degree (at least 3), the two problems are hard to approximate within some constant factor, a question which was open. We summarize all known results in the area, and we compare them to the ones for the related problem Dominating Set. In particular, our work exhibits important graph classes for which Dominating Set is efficiently solvable, but Identifying Code and Locating-Dominating Set are hard (whereas in all previous works, their complexity was the same). We also introduce graph classes for which the converse holds, and for which the complexities of Identifying Code and Locating-Dominating Set differ.

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Section: Related Workmentioning

confidence: 63%

Section: Definitions and Problemsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Min Id Codementioning

confidence: 99%

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Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes

Foucaud

2015

Journal of Discrete Algorithms

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“…In this paper we focus on a combinatorial approach, which is closely related to error-correcting codes, and specifically to identifying codes. Many of the results provided in this paper can be found in [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Localization and identification in networks using robust identifying codes

Laifenfeld

2008

2008 Information Theory and Applications Workshop

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Abstract-Many practical problems in networks such as fault detection and diagnosis, location detection, environmental monitoring, etc, require to identify specific nodes or links based on a set of observations, which size is a subject of optimization. In this paper we focus on a combinatorial approach to these problems, which is closely related to coding techniques, and specifically to identifying codes. The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. In this paper we show efficient reductions between the identifying code problem and well-known covering problems, resulting in a tight hardness of approximation result and provable good centralized and distributed approximations. We further provide empirical and theoretical results on identifying codes in random networks and efficient constructions of these codes in infinite grids.

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Health Monitoring of Critical Power System Equipments Using Identifying Codes

Basu

Padhee

Roy

et al. 2018

Critical Information Infrastructures Security

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High voltage power transformers are one of the most critical equipments in the electric power grid. A sudden failure of a power transformer can significantly disrupt bulk power delivery. Before a transformer reaches its critical failure state, there are indicators which, if monitored periodically, can alert an operator that the transformer is heading towards a failure. One of the indicators is the signal to noise ratio (SNR) of the voltage and current signals in substations located in the vicinity of the transformer. During normal operations, the width of the SNR band is small. However, when the transformer heads towards a failure, the widths of the bands increase, reaching their maximum just before the failure actually occurs. This change in width of the SNR can be observed by sensors, such as phasor measurement units (PMUs) located nearby. Identifying Code is a mathematical tool that enables one to uniquely identify one or more objects of interest, by generating a unique signature corresponding to those objects, which can then be detected by a sensor. In this paper, we first describe how Identifying Code can be utilized for detecting failure of power transformers. Then, we apply this technique to determine the fewest number of sensors needed to uniquely identify failing transformers in different test systems.

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Identifying Codes and Covering Problems

Cited by 42 publications

References 41 publications

Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes

Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes

Localization and identification in networks using robust identifying codes

Health Monitoring of Critical Power System Equipments Using Identifying Codes

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