3 research outputs found
Upward and Orthogonal Planarity are W[1]-hard Parameterized by Treewidth
Upward planarity testing and Rectilinear planarity testing are central
problems in graph drawing. It is known that they are both NP-complete, but XP
when parameterized by treewidth. In this paper we show that these two problems
are W[1]-hard parameterized by treewidth, which answers open problems posed in
two earlier papers. The key step in our proof is an analysis of the
All-or-Nothing Flow problem, a generalization of which was used as an
intermediate step in the NP-completeness proof for both planarity testing
problems. We prove that the flow problem is W[1]-hard parameterized by
treewidth on planar graphs, and that the existing chain of reductions to the
planarity testing problems can be adapted without blowing up the treewidth. Our
reductions also show that the known -time algorithms cannot be
improved to run in time unless ETH fails.Comment: Appears in the Proceedings of the 31st International Symposium on
Graph Drawing and Network Visualization (GD 2023
A new protocol for estimation of woody aboveground biomass in disturbance-prone ecosystems
Almost one third of global drylands are open forests and savannas, which are typically shaped by frequent natural disturbances such as wildfire and herbivory. Studies on ecosystem functions and services of woody vegetation require robust estimates of aboveground biomass (AGB). However, most methods have been developed for comparatively undisturbed forest ecosystems. As they are not tailored to accurately quantify AGB of small and irregular growth forms, their application on these growth forms may lead to unreliable or even biased AGB estimates in disturbance-prone dryland ecosystems. Moreover, these methods cannot quantify AGB losses caused by disturbance agents. Here we propose a methodology to estimate individual-and stand-level woody AGB in disturbance-prone ecosystems. It consists of flexible field sampling routines and estimation workflows for six growth classes, delineated by size and damage criteria. It also comprises a detailed damage assessment, harnessing the ecological archive of woody growth for past disturbances. Based on large inventories collected along steep gradients of elephant disturbances in African dryland ecosystems, we compared the AGB estimates generated with our proposed method against estimates from a less adapted forest inventory method. We evaluated the necessary stepwise procedures of method adaptation and analyzed each step's effect on stand-level AGB estimation. We further explored additional advantages of our proposed method with regard to disturbance impact quantification. Results indicate that a majority of growth forms and individuals in savanna vegetation could only be assessed if methods of AGB estimation were adapted to the conditions of a disturbance-prone ecosystem. Furthermore, our damage assessment demonstrated that one third to half of all woody AGB was lost to disturbances. Consequently, less adapted methods may be insufficient and are likely to render inaccurate AGB estimations. Our proposed method has the potential to accurately quantify woody AGB in disturbance-prone ecosystems, as well as AGB losses. Our method is more time consuming than conventional allometric approaches, yet it can cover sufficient areas within reasonable timespans, and can also be easily adapted to alternative sampling schemes
Dataset on woody aboveground biomass, disturbance losses, and wood density from an African savanna ecosystem
This dataset comprises tree inventories and damage assessments performed in Namibia's semi-arid Zambezi Region. Data were sampled in savannas and savanna woodlands along steep gradients of elephant population densities to capture the effects of those (and other) disturbances on individual-level and stand-level aboveground woody biomass (AGB). The dataset contains raw data on dendrometric measures and processed data on specific wood density (SWD), woody aboveground biomass, and biomass losses through disturbance impacts. Allometric proxies (height, canopy diameters, and in adult trees also stem circumferences) were recorded for n = 6,179 tree and shrub individuals. Wood samples were taken for each encountered species to measure specific wood density. These measurements have been used to estimate woody aboveground biomass via established allometric models, advanced through our improved methodologies and workflows that accounted for tree and shrub architecture shaped by disturbance impacts. To this end, we performed a detailed damage assessment on each woody individual in the field. In addition to estimations of standing biomass, our new method also delivered data on biomass losses to different disturbance agents (elephants, fire, and others) on the level of plant individuals and stands. The data presented here have been used within a study published with Ecological Indicators (Kindermann et al., 2022) to evaluate the benefits of our improved methodology in comparison to a standard reference method of aboveground biomass estimations. Additionally, it has been employed in a study on carbon storage and sequestration in vegetation and soils (Sandhage-Hofmann et al., 2021). The raw data of dendrometric measurements can be subjected to other available allometric models for biomass estimation. The processed data can be used to analyze disturbance impacts on woody aboveground biomass, or for regional carbon storage estimates. The data on species-specific wood density can be used for application to other dendrometric datasets to (re-)estimate biomass through allometric models requiring wood density. It can further be used for plant functional trait analyses. (C) 2022 The Authors. Published by Elsevier Inc