scholarly journals Polyhedra associated with identifying codes in graphs

2018 ◽  
Vol 245 ◽  
pp. 16-27 ◽  
Author(s):  
Gabriela R. Argiroffo ◽  
Silvia M. Bianchi ◽  
Yanina P.Lucarini ◽  
Annegret K. Wagler
Keyword(s):  
Identifying Codes ◽  
Codes In Graphs

Minimum sizes of identifying codes in graphs differing by one edge

2013 ◽  
Vol 6 (2) ◽  
pp. 157-170 ◽  
Author(s):  
Irène Charon ◽  
Iiro Honkala ◽  
Olivier Hudry ◽  
Antoine Lobstein
Keyword(s):  
Identifying Codes ◽  
Codes In Graphs

On a new class of identifying codes in graphs

2007 ◽  
Vol 102 (2-3) ◽  
pp. 92-98 ◽  
Author(s):  
Iiro Honkala ◽  
Tero Laihonen
Keyword(s):  
Identifying Codes ◽  
New Class ◽  
Codes In Graphs

scholarly journals Optimal Identifying Codes in Oriented Paths and Circuits

2021 ◽  
Vol 15 ◽  
pp. 9-14
Author(s):  
Ahmed Semri ◽  
Hillal Touati
Keyword(s):  
Sensor Networks ◽  
Connected Graph ◽  
Multiprocessor Systems ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Identifying Codes ◽  
Identifying Code ◽  
Faulty Processor ◽  
Classical Notion ◽  
Codes In Graphs

Identifying codes in graphs are related to the classical notion of dominating sets [1]. Since there first introduction in 1998 [2], they have been widely studied and extended to several application, such as: detection of faulty processor in multiprocessor systems, locating danger or threats in sensor networks. Let G=(V,E) an unoriented connected graph. The minimum identifying code in graphs is the smallest subset of vertices C, such that every vertex in V have a unique set of neighbors in C. In our work, we focus on finding minimum cardinality of an identifying code in oriented paths and circuits

scholarly journals Locating-Dominating Sets and Identifying Codes in Graphs of Girth at least 5

10.37236/4562 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Camino Balbuena ◽  
Florent Foucaud ◽  
Adriana Hansberg
Keyword(s):  
Minimum Degree ◽  
Dominating Set ◽  
Upper Bounds ◽  
Disjoint Paths ◽  
Minimum Size ◽  
Dominating Sets ◽  
Identifying Codes ◽  
Identifying Code ◽  
Codes In Graphs ◽  
Vertex Disjoint

Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locating-dominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertex-disjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meeting these bounds.

Minimum sizes of identifying codes in graphs differing by one vertex

2013 ◽  
Vol 5 (2) ◽  
pp. 119-136 ◽  
Author(s):  
Irène Charon ◽  
Iiro Honkala ◽  
Olivier Hudry ◽  
Antoine Lobstein
Keyword(s):  
Identifying Codes ◽  
Codes In Graphs

scholarly journals Improved bounds on identifying codes in binary Hamming spaces

2010 ◽  
Vol 31 (3) ◽  
pp. 813-827 ◽  
Author(s):  
Geoffrey Exoo ◽  
Ville Junnila ◽  
Tero Laihonen ◽  
Sanna Ranto
Keyword(s):  
Identifying Codes

scholarly journals Lower Bounds for Identifying Codes in some Infinite Grids

10.37236/394 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Ryan Martin ◽  
Brendon Stanton
Keyword(s):  
Lower Bounds ◽  
Finite Graph ◽  
Infinite Graphs ◽  
Locally Finite ◽  
Identifying Codes ◽  
Identifying Code ◽  
Hexagonal Grids ◽  
Closed Neighborhood ◽  
Definition Of ◽  
Infinite Grids

An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is $|C|/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some small values of $r$ in both the square and hexagonal grids.

scholarly journals General Bounds for Identifying Codes in Some Infinite Regular Graphs

10.37236/1583 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Irène Charon ◽  
Iiro Honkala ◽  
Olivier Hudry ◽  
Antoine Lobstein
Keyword(s):  
Undirected Graph ◽  
Upper Bounds ◽  
Regular Graphs ◽  
Lower And Upper Bounds ◽  
Identifying Codes ◽  
Identifying Code

Consider a connected undirected graph $G=(V,E)$ and a subset of vertices $C$. If for all vertices $v \in V$, the sets $B_r(v) \cap C$ are all nonempty and pairwise distinct, where $B_r(v)$ denotes the set of all points within distance $r$ from $v$, then we call $C$ an $r$-identifying code. We give general lower and upper bounds on the best possible density of $r$-identifying codes in three infinite regular graphs.

Sequences of optimal identifying codes

2002 ◽  
Vol 48 (3) ◽  
pp. 774-776 ◽  
Author(s):  
T.K. Laihonen
Keyword(s):  
Identifying Codes

Robust Localization Using Identifying Codes

2009 ◽  
pp. 321-347
Author(s):  
Moshe Laifenfeld ◽  
Ari Trachtenberg ◽  
David Starobinski
Keyword(s):  
Experimental Data ◽  
Information Theory ◽  
Real Life ◽  
Signal Propagation ◽  
Identifying Codes ◽  
Sensor Failures ◽  
Robust Localization ◽  
Potential Benefits ◽  
Set Up

Various real-life environments are exceptionally harsh for signal propagation, rendering well-known trilateration techniques (e.g. GPS) unsuitable for localization. Alternative proximity-based techniques, based on placing sensors near every location of interest, can be fairly complicated to set up, and are often sensitive to sensor failures or corruptions. The authors propose a different paradigm for robust localization based on identifying codes, a concept borrowed from the information theory literature. This chapter describes theoretical and practical considerations in designing and implementing such a localization infrastructure, together with experimental data supporting the potential benefits of the proposed technique.

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