An Implementation of Indoor Location Detection Systems Based on Identifying Codes

Ungrangsi, Rachanee; Trachtenberg, Ari; Starobinski, David

doi:10.1007/978-3-540-30179-0_16

Cited by 32 publications

(25 citation statements)

References 15 publications

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“…In the LocatingDominating Set problem, we ask for a dominating set S such that the vertices outside of S are distinguished by their neighbourhood within S. In Metric Dimension, we wish to select a set S of vertices of a graph G such that every vertex of G is uniquely identied by its distances to the vertices of S. These problems have been extensively studied since their introduction in the 1970s and 1980s. They have been applied to various areas such as network verication [2], fault-detection in networks [36], graph isomorphism testing [1] or the logical denability of graphs [26].…”

Section: Introductionmentioning

confidence: 99%

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Foucaud

Mertzios

Naserasr

et al. 2016

Graph-Theoretic Concepts in Computer Science

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Abstract. We study the problems Locating-Dominating Set and Metric Dimension, which consist of determining a minimum-size set of vertices that distinguishes the vertices of a graph using either neighbourhoods or distances. We consider these problems when restricted to interval graphs and permutation graphs. We prove that both decision problems are NP-complete, even for graphs that are at the same time interval graphs and permutation graphs and have diameter 2. While Locating-Dominating Set parameterized by solution size is trivially xed-parameter-tractable, it is known that Metric Dimension is W [2]-hard. We show that for interval graphs, this parameterization of Metric Dimension is xed-parameter-tractable.

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Section: Introductionmentioning

confidence: 99%

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Foucaud

Mertzios

Naserasr

et al. 2016

Graph-Theoretic Concepts in Computer Science

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show abstract

“…One of the interests of these notions lies in their applications to the location of threats in facilities [54,58] and error detection in computer networks [40]. One can also mention applications to routing [44], to bioinformatics [37] (where identifying codes are called differentiating dominating sets) and to measuring the first-order logical complexity of graphs [41] (where locating-dominating sets are calledsieves).…”

Section: Definitions and Problemsmentioning

confidence: 99%

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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“…Locating-dominating sets [22,23] and open locating dominating sets [21] are defined in a similar way. These concepts are studied by various authors since the 1970s and 1980s, and have been applied to various regions such as fault-detection in networks [12,25] or graph isomorphism testing [2].…”

Section: Introductionmentioning

confidence: 99%

Identification of points using disks

Gledel¹,

Parreau²

2019

Discrete Mathematics

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We consider the problem of identifying n points in the plane using disks, i.e., minimizing the number of disks so that each point is contained in a disk and no two points are in exactly the same set of disks. This problem can be seen as an instance of the test covering problem with geometric constraints on the tests. We give tight lower and upper bounds on the number of disks needed to identify any set of n points of the plane. In particular, we prove that if there are no three colinear points nor four cocyclic points, then 2⌈n/6⌉ + 1 disks are enough, improving the known bound of ⌈(n + 1)/2⌉ when we only require that no three points are colinear. We also consider complexity issues when the radius of the disks is fixed, proving that this problem is NP-complete. In contrast, we give a linear-time algorithm computing the exact number of disks if the points are colinear.

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An Implementation of Indoor Location Detection Systems Based on Identifying Codes

Cited by 32 publications

References 15 publications

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

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

Identification of points using disks

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