Unified almost linear kernels for generalized covering and packing problems on nowhere dense classes

Let $\mathcal{F}$ be a family of graphs, and let $p,r$ be nonnegative integers. The \textsc{$(p,r,\mathcal{F})$-Covering} problem asks whether for a graph $G$ and an integer $k$, there exists a set $D$ of at most $k$ vertices in $G$ such that $G^p\setminus N_G^r[D]$ has no induced subgraph isomorphic to a graph in $\mathcal{F}$, where $G^p$ is the $p$-th power of $G$. The \textsc{$(p,r,\mathcal{F})$-Packing} problem asks whether for a graph $G$ and an integer $k$, $G^p$ has $k$ induced subgraphs $H_1,\ldots,H_k$ such that each $H_i$ is isomorphic to a graph in $\mathcal{F}$, and for distinct $i,j\in \{1, \ldots, k\}$, the distance between $V(H_i)$ and $V(H_j)$ in $G$ is larger than $r$. We show that for every fixed nonnegative integers $p,r$ and every fixed nonempty finite family $\mathcal{F}$ of connected graphs, the \textsc{$(p,r,\mathcal{F})$-Covering} problem with $p\leq2r+1$ and the \textsc{$(p,r,\mathcal{F})$-Packing} problem with $p\leq2\lfloor r/2\rfloor+1$ admit almost linear kernels on every nowhere dense class of graphs, and admit linear kernels on every class of graphs with bounded expansion, parameterized by the solution size $k$. We obtain the same kernels for their annotated variants. As corollaries, we prove that \textsc{Distance-$r$ Vertex Cover}, \textsc{Distance-$r$ Matching}, \textsc{$\mathcal{F}$-Free Vertex Deletion}, and \textsc{Induced-$\mathcal{F}$-Packing} for any fixed finite family $\mathcal{F}$ of connected graphs admit almost linear kernels on every nowhere dense class of graphs and linear kernels on every class of graphs with bounded expansion. Our results extend the results for \textsc{Distance-$r$ Dominating Set} by Drange et al. (STACS 2016) and Eickmeyer et al. (ICALP 2017), and the result for \textsc{Distance-$r$ Independent Set} by Pilipczuk and Siebertz (EJC 2021).Comment: 38 page

Towards Constant-Factor Approximation for Chordal / Distance-Hereditary Vertex Deletion

For a family of graphs ?, Weighted ?-Deletion is the problem for which the input is a vertex weighted graph G = (V, E) and the goal is to delete S ? V with minimum weight such that G?S ? ?. Designing a constant-factor approximation algorithm for large subclasses of perfect graphs has been an interesting research direction. Block graphs, 3-leaf power graphs, and interval graphs are known to admit constant-factor approximation algorithms, but the question is open for chordal graphs and distance-hereditary graphs. In this paper, we add one more class to this list by presenting a constant-factor approximation algorithm when ? is the intersection of chordal graphs and distance-hereditary graphs. They are known as ptolemaic graphs and form a superset of both block graphs and 3-leaf power graphs above. Our proof presents new properties and algorithmic results on inter-clique digraphs as well as an approximation algorithm for a variant of Feedback Vertex Set that exploits this relationship (named Feedback Vertex Set with Precedence Constraints), each of which may be of independent interest

A Polynomial Kernel for 3-Leaf Power Deletion

For a non-negative integer ?, a graph G is an ?-leaf power of a tree T if V(G) is equal to the set of leaves of T, and distinct vertices v and w of G are adjacent if and only if the distance between v and w in T is at most ?. Given a graph G, 3-Leaf Power Deletion asks whether there is a set S ? V(G) of size at most k such that GS is a 3-leaf power of some treeT. We provide a polynomial kernel for this problem. More specifically, we present a polynomial-time algorithm for an input instance (G,k) to output an equivalent instance (G\u27,k\u27) such that k\u27? k and G\u27 has at most O(k^14) vertices

Three problems on well-partitioned chordal graphs

In this work, we solve three problems on well-partitioned chordal graphs. First, we show that every connected (resp., 2-connected) well-partitioned chordal graph has a vertex that intersects all longest paths (resp., longest cycles). It is an open problem [Balister et al., Comb. Probab. Comput. 2004] whether the same holds for chordal graphs. Similarly, we show that every connected well-partitioned chordal graph admits a (polynomial-time constructible) tree 3-spanner, while the complexity status of the Tree 3-Spanner problem remains open on chordal graphs [Brandstädt et al., Theor. Comput. Sci. 2004]. Finally, we show that the problem of finding a minimum-size geodetic set is polynomial-time solvable on well-partitioned chordal graphs. This is the first example of a problem that is NP -hard on chordal graphs and polynomial-time solvable on well-partitioned chordal graphs. Altogether, these results reinforce the significance of this recently defined graph class as a tool to tackle problems that are hard or unsolved on chordal graphs.acceptedVersio

Retrieval of total precipitable water from Himawari-8 AHI data: A comparison of random forest, extreme gradient boosting, and deep neural network

Total precipitable water (TPW), a column of water vapor content in the atmosphere, provides information on the spatial distribution of moisture. The high-resolution TPW, together with atmospheric stability indices such as convective available potential energy (CAPE), is an effective indicator of severe weather phenomena in the pre-convective atmospheric condition. With the advent of high performing imaging instrument onboard geostationary satellites such as Advanced Himawari Imager (AHI) onboard Himawari-8 of Japan and Advanced Meteorological Imager (AMI) onboard GeoKompsat-2A of Korea, it is expected that unprecedented spatiotemporal resolution data (e.g., AMI plans to provide 2 km resolution data at every 2 min over the northeast part of East Asia) will be provided. To derive TPW from such high-resolution data in a timely fashion, an efficient algorithm is highly required. Here, machine learning approaches-random forest (RF), extreme gradient boosting (XGB), and deep neural network (DNN)-are assessed for the TPW retrieved from AHI over the clear sky in Northeast Asia area. For the training dataset, the nine infrared brightness temperatures (BT) of AHI (BT8 to 16 centered at 6.2, 6.9, 7.3, 8.6, 9.6, 10.4, 11.2, 12.4, and 13.3 ??m, respectively), six dual channel differences and observation conditions such as time, latitude, longitude, and satellite zenith angle for two years (September 2016 to August 2018) are used. The corresponding TPW is prepared by integrating the water vapor profiles from InterimEuropean Centre for Medium-Range Weather Forecasts Re-Analysis data (ERA-Interim). The algorithm performances are assessed using the ERA-Interim and radiosonde observations (RAOB) as the reference data. The results show that the DNN model performs better than RF and XGB with a correlation coefficient of 0.96, a mean bias of 0.90 mm, and a root mean square error (RMSE) of 4.65 mm when compared to the ERA-Interim. Similarly, DNN results in a correlation coefficient of 0.95, a mean bias of 1.25 mm, and an RMSE of 5.03 mm when compared to RAOB. Contributing variables to retrieve the TPW in each model and the spatial and temporal analysis of the retrieved TPW are carefully examined and discussed. ?? 2019 by the authors

Icing detection over East Asia from geostationary satellite data using machine learning approaches

Even though deicing or airframe coating technologies continue to develop, aircraft icing is still one of the critical threats to aviation. While the detection of potential icing clouds has been conducted using geostationary satellite data in the US and Europe, there is not yet a robust model that detects potential icing areas in East Asia. In this study, we proposed machine-learning-based icing detection models using data from two geostationary satellites—the Communication, Ocean, and Meteorological Satellite (COMS) Meteorological Imager (MI) and the Himawari-8 Advanced Himawari Imager (AHI)—over Northeast Asia. Two machine learning techniques—random forest (RF) and multinomial log-linear (MLL) models—were evaluated with quality-controlled pilot reports (PIREPs) as the reference data. The machine-learning-based models were compared to the existing models through five-fold cross-validation. The RF model for COMS MI produced the best performance, resulting in a mean probability of detection (POD) of 81.8%, a mean overall accuracy (OA) of 82.1%, and mean true skill statistics (TSS) of 64.0%. One of the existing models, flight icing threat (FIT), produced relatively poor performance, providing a mean POD of 36.4%, a mean OA of 61.0, and a mean TSS of 9.7%. The Himawari-8 based models also produced performance comparable to the COMS models. However, it should be noted that very limited PIREP reference data were available especially for the Himawari-8 models, which requires further evaluation in the future with more reference data. The spatio-temporal patterns of the icing areas detected using the developed models were also visually examined using time-series satellite data

Detection of tropical overshooting cloud tops using himawari-8 imagery

Overshooting convective cloud Top (OT)-accompanied clouds can cause severe weather conditions, such as lightning, strong winds, and heavy rainfall. The distribution and behavior of OTs can affect regional and global climate systems. In this paper, we propose a new approach for OT detection by using machine learning methods with multiple infrared images and their derived features. Himawari-8 satellite images were used as the main input data, and binary detection (OT or nonOT) with class probability was the output of the machine learning models. Three machine learning techniques-random forest (RF), extremely randomized trees (ERT), and logistic regression (LR)-were used to develop OT classification models to distinguish OT from non-OT. The hindcast validation over the Southeast Asia andWest Pacific regions showed that RF performed best, resulting in a mean probabilities of detection (POD) of 77.06% and a mean false alarm ratio (FAR) of 36.13%. Brightness temperature at 11.2 ??m (Tb11) and its standard deviation (STD) in a 3 ?? 3 window size were identified as the most contributing variables for discriminating OT and nonOT classes. The proposed machine learning-based OT detection algorithms produced promising results comparable to or even better than the existing approaches, which are the infrared window (IRW)-texture and water vapor (WV) minus IRW brightness temperature difference (BTD) methods