An r-identifying code on a graph G is a set C ⊂ V (G) such that for every vertex in V (G), the intersection of the radius-r closed neighborhood with C is nonempty and different. Here, we provide an overview on codes for the n-dimensional lattice, discussing the case of 1-identifying codes, constructing a sparse code for the 4-dimensional lattice as well as showing that for fixed n, the minimum ...

The problem of the r -identifying code of a cycle Cn has been solved totally when n is even. Recently, S. Gravier et al. give the r -identifying code for the cycle Cn with the minimum cardinality for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) 6= 1. In this paper, we deal with the r -identifying code of the cycle Cn for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) = 1. c © 2007 Elsevier Ltd. All rig...

While compiling a native application, different compiler flags or optimization levels can be configured. This choice depends on the requirements. For example, if application binary is intended for final release, and settings should set execution speed efficiency. Alternatively, to used debugging purposes, debug configured accordingly, usually involving minor no code optimization. However, this ...

An important goal for programmers is to minimize cost of identifying and correcting defects in source code. Code review is commonly used for identifying programming defects. However, manual code review has some shortcomings: a) it is time consuming, b) outcomes are subjective and depend on the skills of reviewers. An automated approach for assisting in code reviews is thus highly desirable. We ...

We model a problem about networks built from wireless devices using identifying and locating-dominating codes in unit disk graphs. It is known that minimising the size of an identifying code is NP-complete even for bipartite graphs. First, we improve this result by showing that the problem remains NP-complete for bipartite planar unit disk graphs. Then, we address the question of the existence ...

Let (P ,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = ⋃ x∈X {y : yIx} and by [X] = (X)I ∪ X. With this terminology a partial linear space (P ,L, I) is said to admit a (1,≤ k)-identifying code if and only if the sets [X] are mutually different for all X ⊆ P ∪ L with |X| ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)-i...

An identifying code is a subset of vertices of a graph such that each vertex is uniquely determined by its neighbourhood within the identifying code. If γ(G) denotes the minimum size of an identifying code of a graph G, it was conjectured by F. Foucaud, R. Klasing, A. Kosowski and A. Raspaud that if a connected graph G has n vertices and maximum degree d and admits an identifying code, then γ(G...

Let (P ,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = ⋃ x∈X{y : yIx} and by [X ] = (X)I ∪ X . With this terminology a partial linear space (P ,L, I) is said to admit a (1,≤ k)-identifying code if and only if the sets [X ] are mutually different for all X ⊆ P ∪L with |X | ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)...