Dense Classes Research Articles

Isomorphism, canonization, and definability for graphs of bounded rank width

We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width.

Rainbow independent sets on dense graph classes

Given a family I of independent sets in a graph, a rainbow independent set is an independent set I such that there is an injection ϕ:I→I where for each v∈I, v is contained in ϕ(v). Aharoni et al. (2019) determined for various graph classes C whether C satisfies a property that for every n, there exists N=N(C,n) such that every family of N independent sets of size n in a graph in C contains a rainbow independent set of size n. In this paper, we add two dense graph classes satisfying this property, namely, the class of graphs of bounded neighborhood diversity and the class of r-powers of graphs in a bounded expansion class.

Kernelization and approximation of distance-[formula omitted] independent sets on nowhere dense graphs

For a positive integer r, a distance-r independent set in an undirected graph G is a set I⊆V(G) of vertices pairwise at distance greater than r, while a distance-r dominating set is a set D⊆V(G) such that every vertex of the graph is within distance at most r from a vertex from D. We study the duality between the maximum size of a distance-2r independent set and the minimum size of a distance-r dominating set in nowhere dense graph classes, as well as the kernelization complexity of the distance-r independent set problem on these graph classes. Specifically, we prove that the distance-r independent set problem admits an almost linear kernel on every nowhere dense graph class.

Erdös--Hajnal Properties for Powers of Sparse Graphs

We prove that for every nowhere dense class of graphs $\mathcal{C}$, positive integer $d$, and $\varepsilon>0$, the following holds: in every $n$-vertex graph $G$ from $\mathcal{C}$ one can find two disjoint vertex subsets $A,B\subseteq V(G)$ such that $|A|\geq (1/2-\varepsilon)\cdot n$ and $|B|=\Omega(n^{1-\varepsilon})$; and either ${dist}(a,b)\leq d$ for all $a\in A$ and $b\in B$, or ${dist}(a,b)>d$ for all $a\in A$ and $b\in B$. We also show some stronger variants of this statement, including a generalization to the setting of first-order interpretations of nowhere dense graph classes.

Land Use-Land Cover Change and Its Relationships with the Groundwater Table and the Plants’ Altitudinal Zones: A Case Study of Arsanjan County, Iran

Assessing dynamics in the land use-land cover change (LULCC) is an effective approach for analyzing alterations in the physical and natural features of the farmlands and rangelands. Fifteen Landsat images are utilized to perform the LULCC analysis over Arsanjan County, Iran, for the period of 1987–2017. After dividing the study area into five classes of NDVI, time series of the areas associated with these classes are constructed. The fitted trend lines showed that the extent of dense and moderate vegetation classes has an increasing or decreasing trend over the period of 1987–2003 or 2003–2017, respectively. By comparing trends in the extent of vegetated areas and groundwater table, the mentioned increasing or decreasing trends are attributed to the ever-increasing trends in the groundwater exploitation prior to and after 2003. The post-classification and NDVI differencing methods detect changes between 2003 and 2017. Compared to the NDVI differencing method, the accuracy coefficients are found greater for the post-classification approach. The decrease in the extent of cultivated and swampy lands is mostly counterbalanced by an increase in the areas of barren soils and poor vegetation classes. Application of the differencing method proved that the 2·σ and 0.5·σ levels are the appropriate thresholds for detecting changes in farmlands and rangelands, respectively. Compared to low-elevation farmlands, decline in the extent of vegetated-areas is much less for the high-elevation rangelands. The largest or smallest net decrease in highlands’ vegetation was observed for the elevations between 1750 and 2000 or 2250 and 2500 m above mean sea level, respectively.

Uniform orderings for generalized coloring numbers

The generalized coloring numbers colr(G) (also denoted by scolr(G)) and wcolr(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring number, and have found important theoretical and algorithmic applications. For each distance r, these numbers are determined by an “optimal” ordering of the vertices of G. We study the question of whether it is possible to find a single “uniform” ordering that is “good” for all distances r.We show that the answer to this question is essentially “yes”. Our results give new characterizations of graph classes with bounded expansion and nowhere dense graph classes.

Mapping Change in Spatial Extent and Density of Mangrove Forest at Karachi Coast Using Object Based Image Analysis

Karachi shoreline is more than 135 Km long significant for marine fishery breeding and spawning. During 2005 to 2018 the mangrove forest areas in Karachi increased in extent but declined in density. The main cause of mangrove cover change in this region are coastal region development (port building, industrial area and waterfront project). This study aims to monitor both extent and density changes of mangrove forest at Karachi coast. For this purpose, the Landsat imagery was used of the years 2005 and 2018 covering a span of 14 years. The imageries were processed through Normalized Difference Vegetation Index (NDVI) analysis. Simultaneously, random sample locations were identified for mapping and validation of mangrove forest extent and density during 2005 to 2018. The sample locations were categorized as dense, normal and sparse classes. In the next step, sample locations were plotted on NDVI images to determine mean, minimum and maximum values for each class of mangrove forest. In the final step, the accuracy assessment was done using Kappa statistics. Results show that overall accuracy of 2018 imagery is better than 2005 Landsat imagery. The overall extent of mangrove forest increased in the past years.

Mapping Change in Spatial Extent and Density of Mangrove Forest at Karachi Coast Using Object Based Image Analysis

Karachi shoreline is more than 135 Km long significant for marine fishery breeding and spawning. During 2005 to 2018 the mangrove forest areas in Karachi increased in extent but declined in density. The main cause of mangrove cover change in this region are coastal region development (port building, industrial area and waterfront project). This study aims to monitor both extent and density changes of mangrove forest at Karachi coast. For this purpose, the Landsat imagery was used of the years 2005 and 2018 covering a span of 14 years. The imageries were processed through Normalized Difference Vegetation Index (NDVI) analysis. Simultaneously, random sample locations were identified for mapping and validation of mangrove forest extent and density during 2005 to 2018. The sample locations were categorized as dense, normal and sparse classes. In the next step, sample locations were plotted on NDVI images to determine mean, minimum and maximum values for each class of mangrove forest. In the final step, the accuracy assessment was done using Kappa statistics. Results show that overall accuracy of 2018 imagery is better than 2005 Landsat imagery. The overall extent of mangrove forest increased in the past years.

A New Perspective on FO Model Checking of Dense Graph Classes

We study the first-order (FO) model checking problem of dense graph classes, namely, those that have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes that are FO interpretable in graphs of bounded degree. This characterization allows us to efficiently compute such an FO interpretation for an input graph. As a consequence, we obtain an FPT algorithm for successor-invariant FO model checking on any graph class that is FO interpretable in (or an FO transduction of) a graph class of bounded degree. The approach we use to obtain these results may also be of independent interest.

Complex Aerosol Characterization by Scanning Electron Microscopy Coupled with Energy Dispersive X-ray Spectroscopy

Particulate matter (PM) air pollution is a central concern for public health. Current legislation relies on a mass concentration basis, despite broad acceptance that mass alone is insufficient to capture the complexity and toxicity of airborne PM, calling for additional and more comprehensive measurement techniques. We study to what extent scanning electron microscopy coupled with energy dispersive X-ray spectroscopy (SEM/EDS) can be applied for physicochemical characterization of complex aerosols, and investigate its potential for separating particle properties on a single particle basis, even for nanosized particles. SEM/EDS analysis is performed on impactor samples of laboratory generated aerosols, consisting of either NaCl, Halloysite fibers, soot-like Printex90 agglomerates, or their combination. The analysis is automated and performed as EDS maps, covering a statistically relevant number of particles, with analysis times of approximately one hour/sample. Derived size distributions are compared to scanning mobility particle sizer (SMPS) and electric low-pressure impactor (ELPI) results. A method is presented to estimate airborne number concentrations and size distributions directly from SEM results, within a factor 10 of SMPS and ELPI outcomes. A classification scheme is developed based on elemental composition, providing class-specific information with individual particle statistics on shape, size, and mixing state. This can identify primary particles for source apportionment and enables easy distinction between fibrous and dense particle classes, e.g. for targeted risk assessments. Overall, the SEM/EDS analysis provides a more detailed physicochemical characterization of PM than online measurements, e.g. SMPS and ELPI. The method has the potential to improve assessments of PM exposure and risk, and facilitates source identification, even without prior knowledge at sampling.

Assessment of Soil Organic Carbon Stock under Different Density Classes of Oak (Quercus leucotricophora) Forests in Uttarakhand, India

Soil organic carbon (SOC) is one of the most important and essential constituents of soil. It is the largest reservoir of terrestrial carbon. Here, an investigation was carried for the assessment of Soil Organic Carbon in three different density classes of Oak forest of Chakrata (Distt. Dehradun), Itarna (Distt. Tehri Garhwal) and Lansdowne (Distt. Pauri Garhwal) forest divisions of Uttarakhand. Three soil samples from each forest system at 0-30 cm depth were collected from each density to assess soil organic carbon stock. A total of 81 soil sample were collected in three seasons. In summer season among all three division maximum Soil Organic Carbon was assessed in Chakrata dense forest division (81.65 t ha-1), followed by moderate forest (47.66 t ha-1) and open forest (37.68 t ha-1) of Chakrata forest division. In Lansdowne forest division maximum SOC was found in dense forest (79.82 t ha-1) followed by moderate (48.53 t ha-1) and open forest (35.37 t ha-1) respectively. A similar trend was reported in case of Itarna forest division. Where (78.47 t ha-1) come up to maximum reservoir of SOC followed by moderate forest (46.50 t ha-1) and open forest (34.52 t ha-1) respectively. In rainy season among all three division maximum Soil Organic Carbon was assessed in Chakrata dense forest division (66.24 t ha-1), followed by moderate forest(45.62 t ha-1) and open forest (29.53 t ha-1) of Chakrata forest division. In Lansdowne forest division maximum SOC was found in dense forest (75.48 t ha-1) followed by moderate 48.65 t ha-1) and open forest (22.36 t ha-1) respectively. Similar trend was reported in case of Itarna forest division.In winter season among all three divisions maximum Soil Organic Carbon was assessed in Chakrata dense forest division (81.89 t ha-1), followed by moderate forest (56.62 t ha-1) and open forest (32.32 t ha-1) of Chakrata forest division. In Lansdowne forest division maximum SOC was found in dense forest (81.90 t ha-1) followed by moderate (57.43 t ha-1) and open forest (35.99 t ha-1) respectively. A similar trend was reported in case of Itarna forest division. This study reveals that in the Soil Organic Carbon is maximum in the dense forest followed by moderate and open forest which could be possibly due the more flora and fauna in the dense forest followed by moderate and open forest. Possibly the activities of flora and fauna lead to the addition of more carbon content in the soil. The study demonstrated similar trends of SOC in three different dense, moderate and open density classes of Oak forest. These outcomes of the study may explore the possibility to improve the scientific basis of forest management and land use in the near future.

Estimating aboveground forest carbon density using Landsat 8 and field-based data: a comparison of modelling approaches

ABSTRACTAccurately estimating and mapping forest aboveground carbon density (AGCD) is important for evaluating forest carbon sequestration efficiency and dynamics. This study compares different modelling approaches for estimating AGCD using Landsat 8 Operational Land Imager (OLI) imagery and field forest inventory data. We tested it in Yongshun County, Hunan Province, China. Linear regression (LR) and Random Forest (RF) were used to map crown density (CD). We fitted models with and without CD dummy variables for AGCD estimations. The fitting results and performances of these two types of AGCD models were analysed and compared. There was a difference in the estimation of remote-sensing-based CD models and AGCD models; the coefficients of determination (R2) were 0.66 for LR and 0.84 for RF, respectively, in CD estimations; R2 values were 0.46 for LR and 0.65 for RF, respectively, in AGCD estimations as indicated by basic AGCD models. RF was the best algorithm for CD and AGCD estimations. All of the dummy variable AGCD models provided more accurate AGCD estimates than their basic AGCD counterparts. The dummy variable models (DLR and DRF), which took the observed CD as a dummy variable, were the most accurate for the R2 were 0.61 and 0.85, respectively. The AGCD estimations were significantly overestimated and underestimated by basic AGCD models in thin and dense CD classes, respectively. Nevertheless, none of the AGCD estimates produced by any of the dummy variable models showed this problem. The models that used predicted CD as a dummy variable were more consistent with those that considered observed CD as a dummy variable. The accuracies of AGCD estimations were significantly improved by the dummy variable AGCD models, especially in thin and dense plots; in addition, the CD estimations produced by CD models could be used as dummy variables in AGCD remote-sensing-based models. This work provides that a method considering CD dummy variable in remote sensing-based models was reliable for mapping AGCD at a regional scale.

A Multi-Task Framework for Facial Attributes Classification through End-to-End Face Parsing and Deep Convolutional Neural Networks.

Human face image analysis is an active research area within computer vision. In this paper we propose a framework for face image analysis, addressing three challenging problems of race, age, and gender recognition through face parsing. We manually labeled face images for training an end-to-end face parsing model through Deep Convolutional Neural Networks. The deep learning-based segmentation model parses a face image into seven dense classes. We use the probabilistic classification method and created probability maps for each face class. The probability maps are used as feature descriptors. We trained another Convolutional Neural Network model by extracting features from probability maps of the corresponding class for each demographic task (race, age, and gender). We perform extensive experiments on state-of-the-art datasets and obtained much better results as compared to previous results.

Nowhere Dense Graph Classes and Dimension

Nowhere dense graph classes provide one of the least restrictive notions of sparsity for graphs. Several equivalent characterizations of nowhere dense classes have been obtained over the years, using a wide range of combinatorial objects. In this paper we establish a new characterization of nowhere dense classes, in terms of poset dimension: A monotone graph class is nowhere dense if and only if for every h⩾1 and every e > 0, posets of height at most h with n elements and whose cover graphs are in the class have dimension $$\mathcal{O}(n^\epsilon)$$.

Análise multitemporal de parte da Reserva do Alto Rio Guamá, Paragominas, PA

O objetivo dessa pesquisa foi verificar mudanças na cobertura vegetal de parte da Reserva do Alto Rio Guamá em Paragominas, PA, por meio de índices de vegetação, visando elaborar um panorama multitemporal da degradação ambiental. As imagens foram obtidas da base do INPE e a aquisição de bases vetoriais na base do IBGE. O processamento de imagens foi realizado com o programa ENVI 4.7, onde se utilizou as bandas R5, G4 e B3 para as imagens de 1991 e 2010 e as bandas 6R, 5G e 4B para a imagem de 2016. Foi realizada a reprojeção, recorte por máscara e retificação geométrica por pontos de controle. A classificação do índice de vegetação por diferença normalizada (NDVI) considerou as classes água, sem vegetação, gramíneas, capoeira, floresta secundária e floresta densa, para gerar os índices por área (ha). No intervalo de aproximadamente 25 anos houve redução da cobertura florestal, possivelmente pela expansão de atividades agropecuárias e extração de madeira.

Improving Forest Aboveground Biomass (AGB) Estimation by Incorporating Crown Density and Using Landsat 8 OLI Images of a Subtropical Forest in Western Hunan in Central China

Forest aboveground biomass (AGB) estimation modeling based on remote sensing is an important method for large-scale biomass estimation; the accuracy of the estimation models has been a topic of broad and current interest. In this study, we used permanent sample plot data and Landsat 8 Operational Land Imager (OLI) images of western Hunan. Remote-sensing-based models were developed for different vegetation types, and different crown density classes were incorporated. The linear model, linear dummy variable model, and linear mixed-effects model were used to determine the most effective and accurate method for remote-sensing-based AGB estimation. The results show that the adjusted coefficient of determination (R2adj) and root mean square error (RMSE) of the linear dummy model and linear mixed-effects model were significantly better than those of the linear model; the R2adj increased more than 0.16 and the RMSE decreased more than 2.12 for each vegetation type, and the F-test also showed significant differences between the linear model and linear dummy variable model and between the linear model and linear mixed-effects model. The accuracies of the AGB estimations of the linear dummy variable model and the linear mixed-effects model were significantly better than those of linear model in the thin and dense crown density classes. There were no significant differences in the AGB estimation performance between the linear dummy variable model and linear mixed-effects model; these two models were more flexible and more suitable than the linear model for remote-sensing-based AGB estimation. The results of this study provide a new approach for solving the low-accuracy estimations of linear models.

Lossy Kernels for Connected Dominating Set on Sparse Graphs

For $\alpha > 1$, an $\alpha$-approximate (bi)kernel is a polynomial-time algorithm that takes as input an instance $(I, k)$ of a problem $\mathcal{Q}$ and outputs an instance $(I',k')$ (of a problem $\mathcal{Q}'$) of size bounded by a function of $k$ such that, for every $c\geq 1$, a $c$-approximate solution for the new instance can be turned into a $(c\cdot\alpha)$-approximate solution of the original instance in polynomial time. This framework of lossy kernelization was recently introduced by Lokshtanov and co-authors. We study Connected Dominating Set (and its distance-$r$ variant) parameterized by solution size on sparse graph classes like biclique-free graphs, classes of bounded expansion, and nowhere dense classes. We prove that for every $\alpha>1$, Connected Dominating Set admits a polynomial-size $\alpha$-approximate (bi)kernel on all the aforementioned classes. Our results are in sharp contrast to the kernelization complexity of Connected Dominating Set, which is known to not admit a polynomial kernel even on $2$-degenerate graphs and graphs of bounded expansion, unless ${NP} \subseteq \textsf{coNP/poly}$. We complement our results by the following conditional lower bound. We show that if a class $\mathcal{C}$ is somewhere dense and closed under taking subgraphs, then for some value of $r\in \mathbb{N}$ there cannot exist an $\alpha$-approximate bi-kernel for the (Connected) Distance-$r$ Dominating Set problem on $\mathcal{C}$ for any $\alpha>1$ (assuming ${FPT}\neq{W}[1]$).

Polynomial Kernels and Wideness Properties of Nowhere Dense Graph Classes

Nowhere dense classes of graphs [21, 22] are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness , a concept originating in finite model theory, has proved to be particularly useful. Uniform quasi-wideness is used in many fpt-algorithms on nowhere dense classes. However, the existing constructions showing the equivalence of nowhere denseness and uniform quasi-wideness imply a non-elementary blow up in the parameter dependence of the fpt-algorithms, making them infeasible in practice. As a first main result of this article, we use tools from logic, in particular from a sub-field of model theory known as stability theory, to establish polynomial bounds for the equivalence of nowhere denseness and uniform quasi-wideness. A powerful method in parameterized complexity theory is to compute a problem kernel in a pre-computation step, that is, to reduce the input instance in polynomial time to a sub-instance of size bounded in the parameter only (independently of the input graph size). Our new tools allow us to obtain for every fixed radius r ∈ N a polynomial kernel for the distance- r dominating set problem on nowhere dense classes of graphs. This result is particularly interesting, as it implies that for every class C of graphs that is closed under taking subgraphs, the distance- r dominating set problem admits a kernel on C for every value of r if, and only if, it already admits a polynomial kernel for every value of r (under the standard assumption of parameterized complexity theory that FPT ≠ W[2]).

FPT algorithms for domination in sparse graphs and beyond

We study the parameterized complexity of domination problems on sparse graphs and beyond. The nowhere dense classes of graphs have been proposed as the main model for sparseness that can be utilized algorithmically. The class of d-degenerate graphs is not nowhere dense, yet domination remains fixed-parameter tractable. Both nowhere dense classes of graphs and d-degenerate graph classes are biclique-free classes, meaning there is an integer t such that no graph in the class contains Kt,t as a subgraph. In this paper we show that various domination problems are fixed-parameter tractable on biclique-free classes of graphs. Our algorithms are simple and rely on results from extremal graph theory that bound the number of edges in a t-biclique free graph. In particular, the problems k-Dominating Set, Connectedk-Dominating Set, Independentk-Dominating Set and Minimum Weightk-Dominating Set are shown to be FPT, when parameterized by t+k, on graphs not containing Kt,t as a subgraph. With the exception of Connectedk-Dominating Set all described algorithms are linear in the size of the input graph.

FO model checking on geometric graphs

Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking on nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking on dense classes of graphs or other structures. We study the FO model checking problem on dense graph classes definable by geometric means (intersection and visibility graphs). We obtain new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs. These results use the FPT algorithm by Gajarský et al. for FO model checking on posets of bounded width. We also complement the tractability results by related hardness reductions.