Robust Component-based Network Localization with Noisy Range Measurements

Accurate and robust localization is crucial for wireless ad-hoc and sensor networks. Among the localization techniques, component-based methods advance themselves for conquering network sparseness and anchor sparseness. But component-based methods are sensitive to ranging noises, which may cause a huge accumulated error either in component realization or merging process. This paper presents three results for robust component-based localization under ranging noises. (1) For a rigid graph component, a novel method is proposed to evaluate the graph's possible number of flip ambiguities under noises. In particular, graph's \emph{MInimal sepaRators that are neaRly cOllineaR (MIRROR)} is presented as the cause of flip ambiguity, and the number of MIRRORs indicates the possible number of flip ambiguities under noise. (2) Then the sensitivity of a graph's local deforming regarding ranging noises is investigated by perturbation analysis. A novel Ranging Sensitivity Matrix (RSM) is proposed to estimate the node location perturbations due to ranging noises. (3) By evaluating component robustness via the flipping and the local deforming risks, a Robust Component Generation and Realization (RCGR) algorithm is developed, which generates components based on the robustness metrics. RCGR was evaluated by simulations, which showed much better noise resistance and locating accuracy improvements than state-of-the-art of component-based localization algorithms.Comment: 9 pages, 15 figures, ICCCN 2018, Hangzhou, Chin

On the Enumeration of all Minimal Triangulations

We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where "proper" means that the tree decomposition cannot be improved by removing or splitting a bag

The square of a block graph

AbstractThe square H2 of a graph H is obtained from H by adding new edges between every two vertices having distance two in H. A block graph is one in which every block is a clique. For the first time, good characterizations and a linear time recognition of squares of block graphs are given in this paper. Our results generalize several previous known results on squares of trees

Generalized chordality, vertex separators and hyperbolicity on graphs

Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. A vertex separator set in a graph is a set of vertices that disconnects two vertices. In this paper we study the relation between vertex separator sets, some chordality properties which are natural generalizations of being chordal and the hyperbolicity of the graph. We also give a characterization of being quasi-isometric to a tree in terms of chordality and prove that this condition also characterizes being hyperbolic, when restricted to triangles, and having stable geodesics, when restricted to bigons.Comment: 16 pages, 3 figure

On minimal vertex separators of dually chordal graphs: properties and characterizations

Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs are proved. The first states that a graph is dually chordal if and only if it possesses a spanning tree such that every minimal vertex separator induces a subtree. The second says that a graph is dually chordal if and only if the family of minimal vertex separators is Helly, its intersection graph is chordal and each of its members induces a connected subgraph. We also found adaptations for them, requiring just O(|E(G)|) minimal vertex separators if they are conveniently chosen. We obtain at the end a proof of a known characterization of the class of hereditary dually chordal graphs that relies on the properties of minimal vertex separators.Facultad de Ciencias Exacta

On minimal vertex separators of dually chordal graphs: properties and characterizations

Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) [1] and Gutierrez (1996) [6]. We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs are proved. The first states that a graph is dually chordal if and only if it possesses a spanning tree such that every minimal vertex separator induces a subtree. The second says that a graph is dually chordal if and only if the family of minimal vertex separators is Helly, its intersection graph is chordal and each of its members induces a connected subgraph. We also found adaptations for them, requiring just O(|E(G)|) minimal vertex separators if they are conveniently chosen. We obtain at the end a proof of a known characterization of the class of hereditary dually chordal graphs that relies on the properties of minimal vertex separators.Fil: de Caria, Pablo Jesús. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentin

On minimal vertex separators of dually chordal graphs: properties and characterizations

Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs are proved. The first states that a graph is dually chordal if and only if it possesses a spanning tree such that every minimal vertex separator induces a subtree. The second says that a graph is dually chordal if and only if the family of minimal vertex separators is Helly, its intersection graph is chordal and each of its members induces a connected subgraph. We also found adaptations for them, requiring just O(|E(G)|) minimal vertex separators if they are conveniently chosen. We obtain at the end a proof of a known characterization of the class of hereditary dually chordal graphs that relies on the properties of minimal vertex separators.Facultad de Ciencias Exacta