On strongly identifying codes

Honkala, Iiro; Laihonen, Tero; Ranto, Sanna

doi:10.1016/s0012-365x(01)00357-0

Cited by 51 publications

(26 citation statements)

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“…An identifying code is similar to an OLD, but considers the closed neighborhood of a node v V. Thus, it assumes no malfunction of a detector, a node in D. The requirements for an identifying code are similar to those given in the first section, but are for N [v] = N(v) v. A strongly identifying code, as discussed in [4], on a graph, G, must be able to identify a node with an event whether or not a detection system installed at that node fails to function. Thus, it must simultaneously satisfy the requirements of an identifying code and an OLD.…”

Section: Ilp For Cold Generationmentioning

confidence: 99%

An integer program for Open Locating Dominating sets and its results on the hexagon-triangle infinite grid and other graphs

Sweigart

Presnell

Kincaid

2014

2014 Systems and Information Engineering Design Symposium (SIEDS)

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This paper presents an integer linear program (ILP) for the identification of Open Locating Dominating Sets (OLD) of minimum cardinality and presents several results of the ILP on various graphs. The OLD is similar to an identifying code, but for an open neighborhood instead of closed. The OLD was introduced by Peter Slater and Suk J. Seo in 2010 as a method by which one could identify the location of an event at a node where a node in the set can detect events at adjacent nodes, but cannot detect an event at itself. This is perhaps more clear as a series of factories such that those with intrusion detection devices form an identifying code, but an intruder will disable the system at the factory into which she breaks, if so equipped. There are also applications in other areas such as router networks. This paper continues work by Alison Oldham at the College of William and Mary on the development and implementation of an ILP to identify such OLDs on finite graphs. We demonstrate and compare the results on 100 node randomly generated graphs of various constructions; Erdös-Renyi, Geometric and Scale-Free. We find that most graphs have a density near 1/3. We also explore the use of the ILP to generate OLDs for infinite grids, looking specifically at the hexagonaltriangular grid where we discover a new upper bound of 5/12 on the minimum density OLD for this grid. Finally, we extend this ILP to identify locating dominating sets that simultaneously satisfy open and closed neighborhood criteria, or Closed-Open Locating Dominating sets (COLD).

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Section: Ilp For Cold Generationmentioning

confidence: 99%

An integer program for Open Locating Dominating sets and its results on the hexagon-triangle infinite grid and other graphs

Sweigart

Presnell

Kincaid

2014

2014 Systems and Information Engineering Design Symposium (SIEDS)

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“…We provide an infinite sequence of optimal strongly (1, ≤ l)-identifying codes for every l ≥ 3. The case l = 1 is examined in [9] and no infinite family of optimal codes is known in that case. If l = 2 there exist two infinite families of strongly (1, ≤ 2)-identifying codes [13].…”

Section: A Code C Is Strongly (T ≤ L)-identifying If and Only Ifmentioning

confidence: 99%

“…If this is not the case, that is, malfunctioning processors may send '1' or '0' regardless of their state (which is '1'), then we must require more from the code in order to locate the faulty processors in this case. This situation can be handled with the following concept of strong identification introduced in [9,10,13].…”

Section: Introductionmentioning

confidence: 99%

Optimal Codes for Strong Identification

Laihonen

2002

European Journal of Combinatorics

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“…When a detection device at vertex v can determine if an intruder is in N (v) but will not/can not report if the intruder is at v itself, then we are interested in open-locating-dominating sets as introduced for the k-cubes Q k by Honkala, Laihonen and Ranto [21] and for all graphs by Seo and Slater [26,27]. An open dominating set S ⊆ V (G) is an open-locating-dominating set if for all u and v in V (G) one has u).…”

Section: Introductionmentioning

confidence: 99%

“…A graph G has an open-locating-dominating set when no two vertices have the same open neighborhood, and OLD(G) is the minimum cardinality of such a set. See, for example, [5,16,21,28,29,30,31,32,33]. Lobstein [24] maintains a bibliography, currently with more than 300 entries, for work on these topics.…”

Section: Introductionmentioning

confidence: 99%

Open-independent, open-locating-dominating sets

Seo

Slater

2017

ejgta

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A distinguishing set for a graph G = (V, E) is a dominating set D, each vertex v ∈ D being the location of some form of a locating device, from which one can detect and precisely identify any given "intruder" vertex in V (G). As with many applications of dominating sets, the set D might be required to have a certain property for D , the subgraph induced by D (such as independence, paired, or connected). Recently the study of independent locating-dominating sets and independent identifying codes was initiated. Here we introduce the property of open-independence for openlocating-dominating sets.

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On strongly identifying codes

Cited by 51 publications

References 0 publications

An integer program for Open Locating Dominating sets and its results on the hexagon-triangle infinite grid and other graphs

An integer program for Open Locating Dominating sets and its results on the hexagon-triangle infinite grid and other graphs

Optimal Codes for Strong Identification

Open-independent, open-locating-dominating sets

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