Vertex Cover Gets Faster and Harder on Low Degree Graphs

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637(k) n(O(1)).

GHG footprint of major cities in India

Concentration of greenhouse gases (GHG) in the atmosphere has been increasing rapidly during the last century due to ever increasing anthropogenic activities resulting in significant increases in the temperature of the Earth causing global warming. Major sources of GHG are forests (due to human induced land cover changes leading to deforestation), power generation (burning of fossil fuels), transportation (burning fossil fuel), agriculture (livestock, farming, rice cultivation and burning of crop residues), water bodies (wetlands), industry and urban activities (building, construction, transport, solid and liquid waste). Aggregation of GHG (CO2 and non-CO2 gases), in terms of Carbon dioxide equivalent (CO(2)e), indicate the GHG footprint. GHG footprint is thus a measure of the impact of human activities on the environment in terms of the amount of greenhouse gases produced. This study focuses on accounting of the amount of three important greenhouses gases namely carbon dioxide (CO2), methane (CH4) and nitrous oxide (N2O) and thereby developing GHG footprint of the major cities in India. National GHG inventories have been used for quantification of sector-wise greenhouse gas emissions. Country specific emission factors are used where all the emission factors are available. Default emission factors from IPCC guidelines are used when there are no country specific emission factors. Emission of each greenhouse gas is estimated by multiplying fuel consumption by the corresponding emission factor. The current study estimates GHG footprint or GHG emissions (in terms of CO2 equivalent) for Indian major cities and explores the linkages with the population and GDP. GHG footprint (Aggregation of Carbon dioxide equivalent emissions of GHG's) of Delhi, Greater Mumbai, Kolkata, Chennai, Greater Bangalore, Hyderabad and Ahmedabad are found to be 38,633.2 Gg, 22,783.08 Gg, 14,812.10 Gg, 22,090.55 Gg, 19,796.5 Gg, 13,734.59 Gg and 91,24.45 Gg CO2 eq., respectively. The major contributors sectors are transportation sector (contributing 32%, 17.4%, 13.3%, 19.5%, 43.5%, 56.86% and 25%), domestic sector (contributing 30.26%, 37.2%, 42.78%, 39%, 21.6%, 17.05% and 27.9%) and industrial sector (contributing 7.9%, 7.9%, 17.66%, 20.25%, 1231%, 11.38% and 22.41%) of the total emissions in Delhi, Greater Mumbai, Kolkata, Chennai, Greater Bangalore, Hyderabad and Ahmedabad, respectively. Chennai emits 4.79 t of CO2 equivalent emissions per capita, the highest among all the cities followed by Kolkata which emits 3.29 t of CO2 equivalent emissions per capita. Also Chennai emits the highest CO2 equivalent emissions per GDP (2.55 t CO2 eq./Lakh Rs.) followed by Greater Bangalore which emits 2.18 t CO2 eq./Lakh Rs. (C) 2015 Elsevier Ltd. All rights reserved.

Comparative evaluation of inversion approaches of the radiative transfer model for estimation of crop biophysical parameters

The inversion of canopy reflectance models is widely used for the retrieval of vegetation properties from remote sensing. This study evaluates the retrieval of soybean biophysical variables of leaf area index, leaf chlorophyll content, canopy chlorophyll content, and equivalent leaf water thickness from proximal reflectance data integrated broadbands corresponding to moderate resolution imaging spectroradiometer, thematic mapper, and linear imaging self scanning sensors through inversion of the canopy radiative transfer model, PROSAIL. Three different inversion approaches namely the look-up table, genetic algorithm, and artificial neural network were used and performances were evaluated. Application of the genetic algorithm for crop parameter retrieval is a new attempt among the variety of optimization problems in remote sensing which have been successfully demonstrated in the present study. Its performance was as good as that of the look-up table approach and the artificial neural network was a poor performer. The general order of estimation accuracy for para-meters irrespective of inversion approaches was leaf area index > canopy chlorophyll content > leaf chlorophyll content > equivalent leaf water thickness. Performance of inversion was comparable for broadband reflectances of all three sensors in the optical region with insignificant differences in estimation accuracy among them.