Minimum Connectivity Research Articles

A baseline assessment of hydrologic alteration degree for the Mexican catchments at gauged rivers (2016)

River regime has been modified in several freshwater bodies around the world. This alteration has led to species loss, water pollution, higher or lesser economic profits, changes in magnitude, timing, duration and rate change of flow, among others. Thus, hydrologic alteration assessment allows evaluating the regime parameters so that stakeholders, decision-makers, and dams managers may take efficient actions to mitigate or rehabilitate riparian ecosystems. In the present study, Hydrologic Alteration Indexes on Rivers (IAHRIS, for its acronym in Spanish) and the Mexican standard approach were considered to evaluate 1150 gauged catchments in Mexico and come up with an alteration baseline for 67.03% of the country surface. The comparison may assist stakeholders to propose potential changes in the Mexican standard approach. Results reveal that 232 analyzed catchments can be considered as non-altered according to IAHRIS. In stark contrast, there are 281 non-altered catchments in Mexico in agreement with the official standard approach. Altered catchments are mainly impacted by minimum flow metrics and connectivity discharge. Additionally, the correlation between alteration indexes and 5 socio-economic variables was checked to identify which variables may greatly impact hydrologic alteration evolution or mitigation. From the five selected variables, the Human Development Index is significatively correlated to extreme minimum metrics (p = 0.94) while the Gross Domestic Product to extreme maximum metrics (p = 0.90).

An Improved Heterogeneous Motion Prediction Algorithm for Vehicle-to-Vehicle Message Ferrying in VANETs

In infrastructure-less ad-hoc networks, the nodes can converse directly with other nodes without centralized servers. The vehicular networks are derived from the features of mobile ad-hoc networks (MANETs) whereas the message transmissions between the nodes are direct with each other or through some fixed terminals. But, a unique trademark is that the vehicle-to-vehicle ad-hoc links are poor because of extreme mobility which leads to frequent route breakage that causes emergency message delivery failure. The routing protocols availed in MANETS does not suit due to quick topology changes. The hop selection is based on the best cumulative communication duration that will be failing in some cases. Also, the worst/average case scenario is that the minimum connectivity to the source vehicle is not described in existing approaches. The core idea about the proposed research is to deliver data through an optimum path and to eliminate rupture link during the packet transmission. The system uses the Heterogeneous Motion Guess (HMG) algorithm for vehicular networks to set up a vested path. The HMG will select the relay vehicle's current position is near to the target vehicle plus the vehicle will opt the relay forwarder that has good radio coverage. The link lifetime of the selected hop should be greater than the minimum connectivity duration with the source vehicle. The selected vehicle will append the link expiry time and minimum connectivity duration in Route Demand Dispatch message in a unicast manner. This approach significantly minimizes the hop count numbers and improves the stability of the path. It radically predicts the link life, so the node can decide an alternative vested route. The simulation result shows how well the reactive demand-based HMG affords optimum results in terms of packet transmission success rate, average minimum hop counts, and communication delay.

On the minimum degree of the power graph of a finite cyclic group

The power graph [Formula: see text] of a finite group [Formula: see text] is the undirected simple graph whose vertex set is [Formula: see text], in which two distinct vertices are adjacent if one of them is an integral power of the other. For an integer [Formula: see text], let [Formula: see text] denote the cyclic group of order [Formula: see text] and let [Formula: see text] be the number of distinct prime divisors of [Formula: see text]. The minimum degree [Formula: see text] of [Formula: see text] is known for [Formula: see text], see [R. P. Panda and K. V. Krishna, On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups, Comm. Algebra 46(7) (2018) 3182–3197]. For [Formula: see text], under certain conditions involving the prime divisors of [Formula: see text], we identify at most [Formula: see text] vertices such that [Formula: see text] is equal to the degree of at least one of these vertices. If [Formula: see text], or that [Formula: see text] is a product of distinct primes, we are able to identify two such vertices without any condition on the prime divisors of [Formula: see text].

Minimum algebraic connectivity of graphs whose complements are bicyclic with two cycles

For a graph G = (G(V), G(E)), algebraic connectivity a(G) ≥ 0 is the second smallest e-value (eigenvalue) of the Laplacian matrix of G. It is used to find the connectivity, analyze the diffusion processes, measure the robustness and synchronize the stability of the graphs or networks. In the study of interconnected networks it is necessary to design the interlayers links for the assessment and improvement of the realistic constraints optimally. In this paper, we compute the minimum algebraic connectivity and characterize the corresponding extremal graph in the set of the connected graphs such that the complement of each graph is a bicyclic graph with exactly two cycles.

On minimum algebraic connectivity of graphs whose complements are bicyclic

Abstract The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.

A Landscape Connectivity Approach for Determining Minimum Ecological Lake Level: Implications for Lake Restoration

We proposed a new approach to determine the minimum ecological lake level using a landscape connectivity approach. Using MIKE 21 and ArcGIS software, we simulated the water landscape and corresponding connectivity of Baiyangdian Lake on the North China Plain and analyzed the relationship between landscape connectivity and lake level. The minimum ecological lake level was defined as the breakpoint of the lake level-connectivity curve. Results suggested that the minimum ecological lake level of Baiyangdian Lake is 7.8–8.0 m, below which lake ecosystems become fragmented and potentially fragile. Alternatively, better connectivity at lower lake levels may be achieved by engineered modification of landscape patterns. Such approaches can mitigate the waste of water and economic resources due to excessive reliance on increasing water levels to meet minimum connectivity requirements. This approach provided a new perspective for lake ecosystem restoration of use in water-resource- and landscape management.

Influencia de la actividad petrolera y la ganadería ovina en la cubierta del suelo en una región árida y semiárida de la Patagonia Argentina

La Geografía como ciencia ha provisto el mayor cuerpo teórico para el estudio de las configuraciones que se producen sobre el espacio geográfico. La generación de cartografía que representa las cubiertas de suelo es uno de los usos más importantes de la percepción remota. Se seleccionaron polígonos, con actividad petrolera y ganadera, en las siguientes unidades de paisaje: cañadones, pampas y valles. Los polígonos se utilizaron para evaluar cambios multi-temporales de las cubiertas de suelo y las comunidades vegetales en un período de 15 años. Se realizaron clasificaciones supervisadas y análisis de métricas de paisaje para examinar las posibles causas de estos cambios comparando: i) polígonos sin actividad petrolera ni ganadera (testigo), ii) con actividad petrolera y ganadera, iii) con actividad petrolera y sin actividad ganadera, y iv) sin actividad petrolera y con actividad ganadera. Los resultados obtenidos indicaron que la densidad de parches, el borde total, la densidad de borde y el índice de división de los fragmentos aumentaron en las tres unidades de paisaje, entre 2001 y 2016. El índice de contagio, en cambio, disminuyó. Se observó un incremento del suelo desnudo en las pampas y en los valles occidentales, con un retroceso de las comunidades vegetales dominantes. La densidad de parches en los sitios sin disturbios fue la menor, y en los sitios con ambos disturbios actuando simultáneamente fue máxima. En los sitios sin disturbio el tamaño efectivo de malla fue máximo, mientras que en los sitios con algún disturbio fue menor. Al analizar el efecto del disturbio sobre los elementos del paisaje se observó que su presencia genera la mayor densidad de parches y la mínima conectividad. Los resultados muestran que se produjo un proceso de fragmentación en las coberturas del suelo direccionados por la explotación petrolera y la ganadería ovina, que disminuyen el tamaño de los parches y, por lo tanto, la densidad de los mismos por unidad de superficie.

Consensus using omega in asynchronous systems with unknown membership and degenerative Byzantine failures

We study consensus in asynchronous systems where membership is unknown, and where up to f degenerative Byzantine failures can happen. In our failure model a faulty process can have a Byzantine behavior (i.e., it deviates from its specification), and, furthermore, every faulty process will degenerate such that eventually it will have permanent physical or transmission failures. We present a simple algorithm that solves Consensus using the Omega failure detector and a new broadcast primitive called RFLOB in an asynchronous system with degenerative Byzantine failures, which is optimal with respect to failures because it works when f<n/3. RFLOB guarantees reliable, FIFO and local order broadcast in systems with Byzantine processes and unknown membership. Finally, we present an algorithm that implements an Omega failure detector with unknown membership and minimum connectivity (i.e., communication reliability, and synchrony properties) in a system with degenerative Byzantine failures.

Using Telehealth to Address Pediatric Obesity in Rural Pennsylvania

Introduction: While for adults in Pennsylvania, obesity rates tripled from less than 10% in 1990 to 30% in 2015, the combined rates of overweight, obese, and severely obese children and adolescents in Pennsylvania are projected to approach 37.11% by the end of 2018.Method: Pediatric obesity rates in rural areas tend to be even higher than those in urban areas. Pediatric obesity needs to be addressed, since it is strongly correlated with several chronic diseases. Given the scarcity of resources to manage this trend, innovative population-based approaches are needed. Web-based telehealth, telemedicine, mobile health (mHealth), and telephone conferences have been proposed as solutions to treat and prevent childhood obesity in rural areas; the most suitable solution is through a family-based telemedicine intervention. The purpose of this study is to explore the feasibility of such a telehealth application especially for rural Pennsylvania.Results: Telehealth use in healthcare organizations in Pennsylvania is scarce; however, 92% of Pennsylvania’s school districts meet the minimum internet connectivity standards.Discussions: This article, while acknowledging barriers to the adoption of the internet-based telemedicine resources, discusses solutions for increasing their availability and dissemination in rural Pennsylvania. Current internet connectivity standards in Pennsylvania schools reflect ability to participate in telehealth programs in terms of technological background, but schools are not engaged in such programs. An appraisal of the real-life challenges to implement this modality is critical and will pave the way for advocacy and implementation of useful telehealth services in low-resource areas.

On connectivity, conductance and bootstrap percolation for a random k‐out, age‐biased graph

A uniform attachment graph (with parameter k), denoted Gn,k in the paper, is a random graph on the vertex set [n], where each vertex v makes k selections from [v − 1] uniformly and independently, and these selections determine the edge set. We study several aspects of this graph. Our motivation comes from two similarly constructed, well‐studied random graphs: k‐out graphs and preferential attachment graphs. In this paper, we find the asymptotic distribution of its minimum degree and connectivity, and study the expansion properties of Gn,k to show that the conductance of Gn,k is of order . We also study the bootstrap percolation on Gn,k, where r infected neighbors infect a vertex, and show that if the probability of initial infection of a vertex is negligible compared to then with high probability (whp) the disease will not spread to the whole vertex set, and if this probability exceeds by a sub‐logarithmical factor then the disease whp will spread to the whole vertex set.

Computation of Mesh Node Placements Using DE Approach to Minimize Deployment Cost with Maximum Connectivity

A node placement problem is formulated to ensure maximum connectivity and minimum deployment cost using differential evolution based node placement with traffic weight algorithm. A simulation study is performed to evaluate the performance of the network under four different client distribution patterns (Normal, Uniform, Exponential and Weibull). A maximum throughput of 95.3% and 96.2% of throughput is achieved in normal and weibull distributions than the conventional placement. It is observed from the results that the two distributions have good impact on network performance with minimum deployment cost and maximum connectivity. The packet delivery rate shows a percentage increase of 36.6% compared to the SA based placement scheme in normal distribution. It is also observed that a percentage increase of 28.9% of improvement is achieved when clients are distributed with weibull distribution and minimum end to end delay.

Efficient heuristic algorithm for identifying critical nodes in planar networks

The critical node problem (CNP) removes a limited number of nodes from a network in order to achieve the minimum pair-wise connectivity in the remaining network. In this paper, we present a heuristic algorithm for solving the CNP on planar networks. We propose an efficient method to evaluate the quality of solutions by using special properties of planar networks. This enables us to develop a computationally efficient heuristic algorithm for solving the CNP. The proposed algorithm is tested on randomly generated planar networks. The computational experiments show the superiority of this algorithm compared with other algorithms. Furthermore, we examine how the proposed algorithm can be used for a variant of the CNP, called the cardinality-constrained critical node problem.

The bi-objective critical node detection problem with minimum pairwise connectivity and cost: theory and algorithms

An effective way to analyze and apprehend structural properties of networks is to find their most critical nodes. This paper studies a bi-objective critical node detection problem, denoted as Bi-CNDP. In this variant, we do not make any assumptions on the psychology of decision makers and seek to find a set of solutions which minimize the pairwise connectivity of the induced graph and the cost of removing these critical nodes at the same time. After explicitly stating the formulation of Bi-CNDP, we first prove the NP-hardness of this problem for general graphs and the existence of a polynomial algorithm for constructing the $$\varepsilon $$ -approximated Pareto front for Bi-CNDPs on trees. Then different approaches of determining the mating pool and the replacement pool are proposed for the decomposition-based multi-objective evolutionary algorithms. Based on this, two types of decomposition-based multi-objective evolutionary algorithms (MOEA/D and DMOEA- $$\varepsilon \hbox {C}$$ ) are modified and applied to solve the proposed Bi-CNDP. Numerical experiments on sixteen famous benchmark problems with random and logarithmic weights are firstly conducted to assess different types of the mating pool and the replacement pool. Besides, computational results between two improved algorithms, i.e., I-MOEA/D and I-DMOEA- $$\varepsilon \hbox {C}$$ , demonstrate that they behave differently on these instances and I-DMOEA- $$\varepsilon \hbox {C}$$ shows better performance on the majority of test instances. Finally, a decision-making process from the perspective of minimizing the pairwise connectivity of the induced graph given a constraint on the cost of removing nodes is presented for helping decision makers to identify the most critical nodes for further protection or attack.

Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices

The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G. We characterize, with a new elegant proof, those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Then, given two integers n and p with p ? n - 1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pendant vertices.

The algebraic connectivity of graphs with given circumference

The algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix. Algebraic connectivity is closely related to the traditional vertex (edge) connectivity and it plays an important role in the design of various networks. In this paper, we determine the graph which has the minimum algebraic connectivity among all connected graphs with given circumference.

The flexible socio spatial group queries

A socio spatial group query finds a group of users who possess strong social connections with each other and have the minimum aggregate spatial distance to a meeting point. Existing studies limit to either finding the best group of a fixed size for a single meeting location, or a single group of a fixed size w.r.t. multiple locations. However, it is highly desirable to consider multiple locations in a real-life scenario in order to organize impromptu activities of groups of various sizes. In this paper, we propose Top k Flexible Socio Spatial Group Query (Top k-FSSGQ) to find the top k groups w.r.t. multiple POIs where each group follows the minimum social connectivity constraints. We devise a ranking function to measure the group score by combining social closeness, spatial distance, and group size, which provides the flexibility of choosing groups of different sizes under different constraints. To effectively process the Top k-FSSGQ, we first develop an Exact approach that ensures early termination of the search based on the derived upper bounds. We prove that the problem is NP-hard, hence we first present a heuristic based approximation algorithm to effectively select members in intermediate solution groups based on the social connectivity of the users. Later we design a Fast Approximate approach based on the relaxed social and spatial bounds, and connectivity constraint heuristic. Experimental studies have verified the effectiveness and efficiency of our proposed approaches on real datasets.

A Lower Bound for the Algebraic Connectivity of a Graph in Terms of the Domination Number

We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order n with fixed domination number $$\gamma\leq\frac{n+2}{3}$$ , and finally present a lower bound for the algebraic connectivity in terms of the domination number. We also characterize the minimum algebraic connectivity of graphs with domination number half their order.

Extremal graphs for vertex-degree-based invariants with given degree sequences

For a symmetric bivariable function f(x,y), let the connectivity function of a connected graph G be Mf(G)=∑uv∈E(G)f(d(u),d(v)), where d(u) is the degree of a vertex u. In this paper, we prove that for an escalating (de-escalating) function f(x,y), there exists a BFS-graph with the maximum (minimum) connectivity function Mf(G) among all graphs with a c-cyclic degree sequence π=(d1,d2,…,dn) and dn=1, and obtain the majorization theorem for connectivity function for unicyclic and bicyclic degree sequences. Moreover, some applications of graph invariants based on degree are included.

Complexity dichotomies for the Minimum[formula omitted]-Overlay problem

For a (possibly infinite) fixed family of graphs F, we say that a graph G overlaysF on a hypergraph H if V(H) is equal to V(G) and the subgraph of G induced by every hyperedge of H contains some member of F as a spanning subgraph. While it is easy to see that the complete graph on |V(H)| overlays F on a hypergraph H whenever the problem admits a solution, the MinimumF-Overlay problem asks for such a graph with at most k edges, for some given k∈N. This problem allows to generalize some natural problems which may arise in practice. For instance, if the family F contains all connected graphs, then MinimumF-Overlay corresponds to the Minimum Connectivity Inference problem (also known as Subset Interconnection Design problem) introduced for the low-resolution reconstruction of macro-molecular assembly in structural biology, or for the design of networks.Our main contribution is a strong dichotomy result regarding the polynomial vs. NP-complete status with respect to the considered family F. Roughly speaking, we show that the easy cases one can think of (e.g. when edgeless graphs of the right sizes are in F, or if F contains only cliques) are the only families giving rise to a polynomial problem: all others are NP-complete. We then investigate the parameterized complexity of the problem and give similar sufficient conditions on F that give rise to W[1]-hard, W[2]-hard or FPT problems when the parameter is the size of the solution. This yields an FPT/W[1]-hard dichotomy for a relaxed problem, where every hyperedge of H must contain some member of F as a (non necessarily spanning) subgraph.

Computing Critical Nodes in Directed Graphs

We consider the critical node detection problem (CNDP) in directed graphs, which can be defined as follows. Given a directed graph G and a parameter k , we wish to remove a subset S of at most k vertices of G such that the residual graph G ∖ S has minimum pairwise strong connectivity. This problem is NP-hard, and thus we are interested in practical heuristics. In this article, we apply the framework of Georgiadis et al. (SODA 2017) and provide a sophisticated linear-time algorithm for the k =1 case. Based on this algorithm, we provide an efficient heuristic for the general case. Then, we conduct a thorough experimental evaluation of various heuristics for CNDP. Our experimental results suggest that our heuristic performs very well in practice, both in terms of running time and of solution quality.