Edge Cover Research Articles

On Constrained Minimum Weight Edge Covers With Applications to Emergency Planning

ABSTRACTIn this paper we present a new covering problem, called Min Cost ‐Single Location Cover, where we are given a fixed positive integer , a finite ground set , an integral positive demand for each element , a collection of subsets of , an integral positive cost and an integral positive capacity value for each subset . The task is to choose sets from , with multiple choices being allowed, such that each element is covered at least times. However, if a given subset is chosen to cover an element, it must already cover the entire demand of the element. Moreover, each subset may only cover up to of its elements, where again multiple choices are allowed. Our problem is motivated by a healthcare application for placing emergency doctors into facilities such that all emergencies occurring in a shift can be handled in a satisfactory manner. We show that Min Cost ‐Single Location Cover can be solved in polynomial time for , but is strongly NP‐complete for . To handle the case where equals two, we introduce a new constrained ‐edge cover problem in an edge‐colored graph, called Minimum Weight ‐Edge Cover with Colors. We analyze the complexity of this problem for general graphs as well as for the special instances resulting from an instance of ‐Single Location Cover.

The Influence of Bias Voltage and Gas Pressure on Edge Covering during the Arc-PVD Deposition of Hard Coatings

The Influence of Bias Voltage and Gas Pressure on Edge Covering during the Arc-PVD Deposition of Hard Coatings

Mathematical Models for the Single-Channel and Multi-Channel PMU Allocation Problem and Their Solution Algorithms

Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power grid node; thus, the lowest PMU number is optimally selected for the full observation of the entire network. In this study, the PMU placement model is reconsidered, taking into account single- and multi-capacity placement models rather than the well-studied PMU placement model with an unrestricted number of channels. A restricted number of channels per monitoring device is used, instead of supposing that a PMU is able to observe all incident buses through the transmission connectivity lines. The optimization models are declared closely to the power dominating set and minimum edge cover problem in graph theory. These discrete optimization problems are directly related with the minimum set covering problem. Initially, the allocation model is declared as a constrained mixed-integer linear program implemented by mathematical and stochastic algorithms. Then, the 0/1 integer linear problem is reformulated into a non-convex constraint program to find optimality. The mathematical models are solved either in binary form or in the continuous domain using specialized optimization libraries, and are all implemented in YALMIP software in conjunction with MATLAB. Mixed-integer linear solvers, nonlinear programming solvers, and heuristic algorithms are utilized in the aforementioned software packages to locate the global solution for each instance solved in this application, which considers the transformation of the existing power grids to smart grids.

Parallel Acyclic Joins: Optimal Algorithms and Cyclicity Separation

We study equi-join computation in the massively parallel computation (MPC) model. Currently, a main open question under this topic is whether it is possible to design an algorithm that can process any join with load O(N polylog N/p 1/ρ* ) — measured in the number of words communicated per machine — where N is the total number of tuples in the input relations, ρ * is the join’s fractional edge covering number, and p is the number of machines. We settle the question in the negative for the class of tuple-based algorithms (all the known MPC join algorithms fall in this class) by proving the existence of a join query with ρ * = 2 that requires a load of Ω ( N/p 1/3 ) to evaluate. Our lower bound provides solid evidence that the “AGM bound” alone is not sufficient for characterizing the hardness of join evaluation in MPC (a phenomenon that does not exist in RAM). The hard join instance identified in our argument is cyclic, which leaves the question of whether O(N polylog N/p 1/ρ* ) is still possible for acyclic joins. We answer this question in the affirmative by showing that any acyclic join can be evaluated with load O(N / p 1/ρ* ), which is asymptotically optimal (there are no polylogarithmic factors in our bound). The separation between cyclic and acyclic joins is yet another phenomenon that is absent in RAM. Our algorithm owes to the discovery of a new mathematical structure — we call “canonical edge cover” — of acyclic hypergraphs, which has numerous non-trivial properties and makes an elegant addition to database theory.

Approximate core allocations for edge cover games

Edge cover games are cooperative cost games arising from edge cover problems. In an edge cover game, each player controls a vertex and the cost of a coalition is the minimum weight of edge covers in the subgraph induced by the coalition. The approximate core is a relaxation of the core which is one of the most important concepts in cooperative game theory. A vector belongs to the α-core (0≤α≤1) if it recovers at least α-fraction of the total cost of the game when no deviating coalition is better off. In this paper, we show that the 34-core of edge cover games is always non-empty and a vector in the 34-core can be computed efficiently. We also show that 34 is the best constant ratio for the approximate core of edge cover games, as it is the reciprocal of the integrality gap for edge cover problems.

New algebraic and geometric characterizations of planar quintic Pythagorean-hodograph curves

The aim of this work is to provide new characterizations of planar quintic Pythagorean-hodograph curves. The first two are algebraic and consist of two and three equations, respectively, in terms of the edges of the Bézier control polygon as complex numbers. These equations are symmetric with respect to the edge indices and cover curves with generic as well as degenerate control polygons. The last two characterizations are geometric and rely both on just two auxiliary points outside the control polygon. One requires two (possibly degenerate) quadrilaterals to be similar, and the other highlights two families of three similar triangles. All characterizations are a step forward with respect to the state of the art, and they can be linked to the well-established counterparts for planar cubic Pythagorean-hodograph curves. The key ingredient for proving the aforementioned results is a novel general expression for the hodograph of the curve.

Extension of some edge graph problems: Standard, parameterized and approximation complexity

We consider extension variants of some edge optimization problems in graphs containing the classical Edge Cover, Matching, and Edge Dominating Set problems and generalizations thereof. Given a graph G=(V,E) and an edge set U⊆E, it is asked whether there exists an inclusion-wise minimal (or maximal, respectively) feasible solution E′ which satisfies a given property, for instance, being an edge dominating set (or a matching, respectively) and containing the forced edge set U (or avoiding any edges from the forbidden edge set E∖U, respectively). We present hardness results for these problems, for restricted instances such as bipartite or planar graphs. We counter-balance these negative results with parameterized complexity results. We also consider the price of extension, a natural optimization problem variant of extension problems, leading to some approximation and inapproximability results.

Intraspecific variation in sensitivity to habitat fragmentation is influenced by forest cover and distance to the range edge

The relative effects of habitat loss and fragmentation on biodiversity have been a topic of discussion for decades. While it is acknowledged that habitat amount can mediate the effects of habitat fragmentation, it is unclear what other factors may drive inter- and intraspecific variation in fragmentation effects and their implications for conservation. We tested whether the effects of forest fragmentation on 362 bird species' occurrence in the Atlantic Forest of Brazil are mediated by distance to geographic range edge and habitat amount, and whether these effects explain intraspecific variation across populations. Using a single binomial linear mixed effects model, we found that fragmentation had mostly negative effects on occurrence probability up to 1080 km from the species' range edge, independent of habitat amount. We also show that above this distance, fragmentation has predominantly positive effects, more accentuated in deforested landscapes. We demonstrate that fragmentation effects can be both positive and negative, indicating that different populations of the same species can respond differently depending on distance to range edge and local forest cover. Our results help clarify one of the drivers of contradictory results found in the fragmentation literature and highlight the importance of preventing habitat fragmentation for the conservation of endangered populations. Conservation initiatives should focus on minimising fragmentation closer to range edges of target species and in regions where species range edges overlap.

Self centered interval-valued intuitionistic fuzzy graph with an application

In comparison to conventional fuzzy sets, the idea of intervalvalued intuitionistic fuzzy sets provides a more accurate definition of uncertainty. Defuzzification is the aspect of fuzzy control that requires the most processing. It has numerous applications in fuzzy control. In this paper, the concepts strength, length, distance, eccentricity, radius, diameter, centred, selfcentered, path cover, and edge cover of an interval-valued intuitionistic fuzzy graph (IVIFG) are defined in this work. Further, we introduce the definition of a self-centered IVIFG and the necessary and sufficient conditions for an IVIFG to be self-centered are given. Moreover, we investigate some properties of self-centered IVIFG with an illustration and we have discussed applications in IVIFG.

A scheduling algorithm for heterogeneous computing systems by edge cover queue

In heterogeneous computing systems, excellent task scheduling algorithms can shorten the task completion time and improve system parallelism. With the large-scale deployment of edge computing, the task scheduling algorithm in heterogeneous edge computing servers has become a critical factor in improving the overall system performance. This paper proposes a new task scheduling algorithm called the edge cover scheduling algorithm (ECSA), which schedules tasks based on the edge cover queue of the directed acyclic graph (DAG) for heterogeneous computing systems. Based on the estimation of distribution algorithm (EDA) and the graph random walk algorithm, the ECSA generates an edge cover queue from DAG. Then, the ECSA uses the heuristics greedy method with low time and computational complexity to allocate the edge cover queue to processors. Theoretical analysis and simulation results on random DAGs and real-world DAGs show that the ECSA can achieve better scheduling results in terms of makespan, the schedule length ratio (SLR), efficiency, and frequency of best results with low time and computational complexity.

Habitat productivity and anthropogenic development drive rangewide variation in striped skunk (Mephitis mephitis) abundance

Non-charismatic species are often understudied, despite having unique ecological roles that are important to understand and value for ecosystem integrity, function, and health. Striped skunks (Mephitis mephitis) are one such species, as they are stigmatized and feared due to their noxious smell and potential for spreading rabies. Yet this species often co-occurs with humans, occupying a distinct but poorly understood ecological niche. To better understand this understudied species and its unique niche, we used a Bayesian N-mixture model to estimate factors driving the local abundance of striped skunks at a continent-wide scale using data from the Snapshot USA programs in 2019 and 2020. In our modelling approach, we included factors that we a-priori hypothesized would affect striped skunk local abundance, including habitat, agriculture, primary productivity, and anthropogenic factors. We found that skunks were most abundant in more productive and anthropogenically affected areas. The factors driving abundance (in order of effect) were primary productivity, impervious surface, cultivated land, and cultivated-wetland edge cover. While our results underscore striped skunks’ role as a synanthropic species that co-occurs with humans, they are more of a synanthropic misanthrope, as their close relationship with people often causes them to suffer persecution and death. But their relationship with highly productive areas also highlights how striped skunks are habitat generalists that exploit resources in many different types of habitats. Our analysis highlights the importance of programs like Snapshot USA that collect standardized data across large geographic areas and allow broad-scale studies for evaluating the local abundance of understudied species. Using these data, we were able to provide foundational information on the relative importance of the major factors affecting the local abundance of striped skunks, with implications for the management and conservation of this unique and understudied mesocarnivore across its range.

Approximating activation edge-cover and facility location problems

What approximation ratio can we achieve for the Facility Location problem if whenever a client u connects to a facility v, the opening cost of v is at most θ times the service cost of u? We show that this and many other problems are a particular case of the Activation Edge-Cover problem. Here we are given a multigraph G=(V,E), a set R⊆V of terminals, and thresholds {tue,tve} for each uv-edge e∈E. The goal is to find an assignment a={av:v∈V} to the nodes minimizing ∑v∈Vav, such that the edge set Ea={e=uv:au≥tue,av≥tve} activated by a covers R. We obtain ratio 1+maxx≥1⁡ln⁡x1+x/θ≈ln⁡θ−ln⁡ln⁡θ for the problem, where θ≤maxe∈E⁡max⁡{tue,tve}min⁡{tue,tve} is a problem parameter. This result is based on a simple generic algorithm for the problem of minimizing a sum of a decreasing and a sub-additive set functions, which is of independent interest. As an application, we get the same ratio for the above variant of Facility Location. If for each facility all service costs are identical then we show a better ratio 1+maxk∈N⁡Hk−11+k/θ, where Hk=∑i=1k1/i. For the Min-Power Edge-Cover problem we improve the ratio 1.406 of [4] (achieved by iterative randomized rounding) to 1.2785. For unit thresholds we improve the ratio 73/60≈1.217 of [4] to 15551347≈1.155.

Symbolic defects of edge ideals of unicyclic graphs

We introduce the concept of minimum edge cover for an induced subgraph in a graph. Let [Formula: see text] be a unicyclic graph with a unique odd cycle and [Formula: see text] be its edge ideal. We compute the exact values of all symbolic defects of [Formula: see text] using the concept of minimum edge cover for an induced subgraph in a graph. We describe one method to find the quasi-polynomial associated with the symbolic defects of edge ideal [Formula: see text]. We classify the class of unicyclic graphs when some power of maximal ideal annihilates [Formula: see text] for any fixed [Formula: see text]. Also for those class of graphs, we compute the Hilbert function of the module [Formula: see text] for all [Formula: see text]

Completeness-Resolvable Graphs

Given a connected graph \(G=(V(G), E(G))\), the length of a shortest path from a vertex u to a vertex v is denoted by d(u, v). For a proper subset W of V(G), let m(W) be the maximum value of d(u, v) as u ranging over W and v ranging over \(V(G)\setminus W\). The proper subset \(W=\{w_1,\ldots ,w_{|W|}\}\) is a completeness-resolving set of G if $$\begin{aligned} \Psi _W: V(G)\setminus W \longrightarrow [m(W)]^{|W|},\qquad u\longmapsto (d(w_1,u),\ldots ,d(w_{|W|},u)) \end{aligned}$$is a bijection, where $$\begin{aligned}{}[m(W)]^{|W|}=\{(a_{(1)},\ldots ,a_{(|W|)})\mid 1\le a_{(i)}\le m(W)\text { for each }i=1,\ldots ,|W|\}. \end{aligned}$$A graph is completeness-resolvable if it admits a completeness-resolving set. In this paper, we first construct the set of all completeness-resolvable graphs by using the edge coverings of some vertices in given bipartite graphs, and then establish posets on some subsets of this set by the spanning subgraph relationship. Based on each poset, we find the maximum graph and give the lower and upper bounds for the number of edges in a minimal graph. Furthermore, minimal graphs satisfying the lower or upper bound are characterized.

On the unimodality of average edge cover polynomials

The edge cover polynomial of a graph G is the function E(G,x)=∑i≥1e(G,i)xi, where e(G,i) is the number of edge coverings of G with size i. In this paper, we show that the average edge cover polynomial of order n is reduced to the edge cover polynomial of complete graph Kn, based on which we establish that the average edge cover polynomial of order n is unimodal and has at least n−3 non-real roots.

Properties of Large 2-Crossing-Critical Graphs

A $c$-crossing-critical graph is one that has crossing number at least $c$ but each of its proper subgraphs has crossing number less than $c$. Recently, a set of explicit construction rules was identified by Bokal, Oporowski, Richter, and Salazar to generate all large $2$-crossing-critical graphs (i.e., all apart from a finite set of small sporadic graphs). They share the property of containing a generalized Wagner graph $V_{10}$ as a subdivision. In this paper, we study these graphs and establish their order, simple crossing number, edge cover number, clique number, maximum degree, chromatic number, chromatic index, and treewidth. We also show that the graphs are linear-time recognizable and that all our proofs lead to efficient algorithms for the above measures. Keywords. Crossing number, crossing-critical graph, chromatic number, chromatic index, treewidth.

Ocelot density and habitat use in Tamaulipan thornshrub and tropical deciduous forests in Northeastern México

AbstractNortheastern México is one of the most diverse regions in the country with high mammal richness. This region also sits on the northern periphery of the geographic distribution of ocelots (Leopardus pardalis), which are listed as endangered in México. Ocelot ecology in northeastern México is poorly known at local and landscape levels, especially in the ecologically rich temperate sierras, a perceived stronghold for ocelots. We used an occupancy approach to estimate ocelot-habitat use in Tamaulipan thornshrub and tropical deciduous forests and a spatially explicit capture–recapture (SECR) framework to estimate density of ocelots in the northern edge of the Sierra Tamaulipas, México. From May to December 2009, we conducted two camera trap surveys (summer: 20 camera stations; fall: 58 camera stations) on Rancho Caracol and Rancho Camotal, north of the Rio Soto de La Marina. We found ocelot detections were higher in areas with increasing patch density of tropical deciduous forest and habitat use was greater in Tamaulipan thornshrub and tropical deciduous forests with lower edge densities. Ocelot densities varied by sex, with females achieving greater densities (7.88 ocelots/100 km2 [95% CI: 4.85–12.81]) than males (3.81 ocelots/100 km2 [95% CI: 1.96–7.43]). Ocelots were averse to areas with high densities of edge cover in each woody community, supporting the notion of a forest patch interior species. Despite the study occurring 11 years ago, population densities were also among the highest reported in México using spatially explicit capture–recapture methods, The high ecological integrity of the habitat within the Sierra de Tamaulipas, recent protection as a Biosphere Reserve, and remote rugged terrain suggest long-term security of the ocelot population in this region.

Habitat suitability modelling to improve conservation status of two critically endangered endemic Afromontane forest bird species in Taita Hills, Kenya

Tropical montane forests are known to support many endemic species with restricted geographic ranges. Many of these species are however, faced with numerous threats, most notably from habitat loss and degradation, invasive alien species, and climate change. Examples include Taita Apalis and Taita Thrush. Taita Apalis (Apalis fuscigularis) and Taita Thrush (Turdus helleri) are species of birds listed as Critically Endangered by the Government of Kenya and the International Union for Conservation of Nature (IUCN). They are endemic to Taita Hills’ cloud forests in southeastern Kenya and protected under Wildlife Conservation and Management Act. As they face high risk of extinction, exploring their habitat suitability is imperative for their protection. To determine the current spatial distribution and the key ecogeographical explanatory factors and conditions affecting species distribution and indirect effects on species survival and reproduction, we employed Maximum Entropy (MaxEnt) modelling. This study was conducted in Ngangao and Vuria forests in June and July 2019 and 2020. Ngangao forest is gazetted as forest reserve and managed by the Kenya Forest Service whereas Vuria is non-gazetted and thus remains without official protection status. Ecogeographical explanatory variables; climatic, remote sensing-, LIDAR-, topography- and landscape-based variables were used in modelling and separate models were produced. 23 occurrence records of Taita Apalis and 30 of Taita Thrush from Ngangao and 21 of Taita Apalis from Vuria forests were used in the modelling. According to the models, less than 7% of the total area of Ngangao and Vuria forests was predicted as suitable habitat for Taita Apalis and Taita Thrush. This shows that these two species are more vulnerable to extinction from demographic stochasticity. Consequently, managing their habitats is critical for their long-term persistence. LIDAR-based canopy height range and elevation greatly influenced Taita Apalis distribution in Ngangao forest, with areas of high elevation (1620–1750 m a.s.l.) and having open middle-storey preferred. Elevation, slope and topographic wetness index (twi) were the major determinants of Taita Thrush distribution in Ngangao, where gentle sloping areas with moderately dry surfaces within high elevation (1620–1730 m a.s.l.) were favoured. Mean annual temperature, Euclidean distance to the forest edge, slope and land cover type greatly influenced the distribution of Taita Apalis in Vuria, with gentle sloping areas within forest interior made up of indigenous vegetation preferred. This study proposes reforesting open and degraded sites next to areas predicted as highly suitable for the two species; establishment of agroforestry belts based on indigenous trees on the boundaries of the two forests to reduce grazing and firewood collection pressure and enhance resilience to the edge effects; and enhancing forest protection through Participatory Forest Management.

Tallgrass prairie wildlife exposure to spray drift from commonly used soybean insecticides in Midwestern USA

Insecticides are widely used in the Midwestern USA to combat soybean aphids (Aphis glycines), a globally important crop pest. Broad-spectrum foliar insecticides such as chlorpyrifos, lambda-cyhalothrin, and bifenthrin (hereafter, “target insecticides”) are toxic to wildlife in laboratory settings; however, little information exists regarding drift and deposition of these insecticides in fragmented tallgrass prairie grasslands such as those in Minnesota, USA. To address this information gap, target insecticide spray drift and deposition were measured on passive samplers and arthropods in grasslands adjacent to crop fields in Minnesota. Samples were collected at focal soybean field sites immediately following target insecticide application and at reference corn field sites without target insecticide application. Target insecticides were detected 400 m into grasslands at both focal and reference sites. Residues of chlorpyrifos, an insecticide especially toxic to pollinators and birds, were measured above the contact lethal dose (LD50) for honey bees (Apis mellifera) up to 25 m from field edges in adjacent grasslands. Chlorpyrifos residues on arthropods were below the acute oral LD50 for several common farmland bird species but were above the level shown to impair migratory orientation in white-crowed sparrows (Zonotrichia leucophrys). Deposition of target insecticides on passive samplers was inversely associated with distance from field edge and percent canopy cover of grassland vegetation, and positively associated with samplers placed at mid-canopy compared to ground level. Target insecticide deposition on arthropods had an inverse relationship with vertical vegetation density and was positively associated with maximum height of vegetation. Tallgrass prairie with cover ≥25 m from row crop edges may provide wildlife habitat with lower exposure to foliar application insecticides. Prairie management regimes that increase percent canopy cover and density of vegetation may also reduce exposure of wildlife to these insecticides.

A thin and flexible scanner for fingerprints and documents based on metal halide perovskites

Solution-processed photodetectors could be of use in large-area light-sensing applications because they can be fabricated at low cost on plastic substrates and their absorption spectra can be tuned by chemical design. However, fabricating photodetectors with low dark currents and integrating them into high-resolution backplanes remains challenging. Here we show that solution-processed metal halide perovskite photodiodes on top of an amorphous indium gallium zinc oxide transistor backplane can be used to create a flexible image sensor that is ~100 μm thick and has a resolution of 508 pixels per inch. We have developed a pixel edge cover layer for the system that reduces electrode current leakage and thus dark current density. The low noise current in combination with high external quantum efficiency results in high photodetectivity at wavelengths from 550 nm to 770 nm. We show that our imager can be used for document scanning and biometric fingerprinting and that it can be wrapped around objects with radii as small as 0.6 cm. Low-dark-current perovskite photodetectors can be integrated with an oxide transistor backplane to create a high-resolution optical scanning array capable of imaging flat and curved surfaces.