A set S of vertices of a graph G is a dominating set of G if every vertex u of G is either in S or it has a neighbour in S. In other words S is dominating if the sets S ∩N [u] where u ∈ V (G) and N [u] denotes the closed neighbourhood of u in G, are all nonempty. A set S ⊆ V (G) is called a locating code in G, if the sets S ∩ N [u] where u ∈ V (G) \ S are all nonempty and distinct. A set S ⊆ V ...

A partition Π of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of Π. The partition dimension of G is the minimum cardinality of a locating partition of G. A pair of vertices u, v of a graph G are called twins if they have exactly the same set of neighbors other than u and v. A twin class is a ...

Locating the boundary of a head in a head-and-shoulders image is an important problem in model based coding. An approach to this problem using adaptive contour models or 'snakes' is presented. The paper provides a tutorial introduction to the theory of snakes and shows in some detail how they may be implemented using a finite difference method. Some experimental results are presented showing sn...

A set D of vertices in a graph G is 2-dominating if every vertex not in D has at least two neighbors in D and locating-dominating if for every two vertices u, v not in D, the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The minimum cardinality of a 2-dominating set (locatingdominating set) is denoted by γ2(G) (γL(G)). It is known that every tree T with n ≥ 2 vertices, leaves, s suppo...

Assume that G = (V, E) is an undirected graph with vertex set V and edge set E. The ball Br(v) denotes the vertices within graphical distance r from v. A subset C ⊆ V is called an (r,≤ l)-locating-dominating code of type B if the sets Ir(F ) = ⋃ v∈F (Br(v)∩C) are distinct for all subsets F ⊆ V \C with at most l vertices. A subset C ⊆ V is an (r,≤ l)-locatingdominating code of type A if sets Ir(...

This work aims to build a semantic framework for automated debugging. A debugging process consists of tracing, locating, and fixing processes consecutively. The first two processes are accomplished by a tracing procedure and a locating procedure, respectively. The tracing procedure reproduces the execution of a failed test case with well-designed data structures and saves necessary information ...

Given a set of n points P in the Euclidean plane, we consider the problem of locating a 1-corner polygonal chain X such that minp∈P d(p,X) is maximized. The polygonal chain has the added property that its interior angle is α and it partitions P . In this note we present an algorithm that solves the problem in o(n) time and space. The previous best running time for this problem was O(n log n) ti...

Given a set of n points P in the Euclidean plane, we consider the problem of locating a 1-corner polygonal chain X such that minp∈P d(p, X) is maximized. The polygonal chain has the added property that its interior angle is α and it partitions P . In this note we present an algorithm that solves the problem in o(n) time and space. The previous best running time for this problem was O(n log n) t...

We consider the problem of locating a light coin out of a set containing n coins, n ? 1 of which have the same weight. The weighing device is a balance with r 2 pans and, when r equally sized subset of coins are weighted, it indicates the eventual subset containing the light coin. We give an algorithm to nd the counterfeit coin that requires the minimum possible average number of weighings. All...