Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

We present a distributed algorithm that finds a maximal edge packing in O(Δ + log* W) synchronous communication rounds in a weighted graph, independent of the number of nodes in the network; here Δ is the maximum degree of the graph and W is the maximum weight. As a direct application, we have a distributed 2-approximation algorithm for minimum-weight vertex cover, with the same running time. We also show how to find an f-approximation of minimum-weight set cover in O(f2k2 + fk log* W) rounds; here k is the maximum size of a subset in the set cover instance, f is the maximum frequency of an element, and W is the maximum weight of a subset. The algorithms are deterministic, and they can be applied in anonymous networks.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

Monitoring Indigenous Tropical Montane Forests in the Taita Hills Using Airborne Digital Camera Imagery

The loss and degradation of forest cover is currently a globally recognised problem. The fragmentation of forests is further affecting the biodiversity and well-being of the ecosystems also in Kenya. This study focuses on two indigenous tropical montane forests in the Taita Hills in southeastern Kenya. The study is a part of the TAITA-project within the Department of Geography in the University of Helsinki. The study forests, Ngangao and Chawia, are studied by remote sensing and GIS methods. The main data includes black and white aerial photography from 1955 and true colour digital camera data from 2004. This data is used to produce aerial mosaics from the study areas. The land cover of these study areas is studied by visual interpretation, pixel-based supervised classification and object-oriented supervised classification. The change of the forest cover is studied with GIS methods using the visual interpretations from 1955 and 2004. Furthermore, the present state of the study forests is assessed with leaf area index and canopy closure parameters retrieved from hemispherical photographs as well as with additional, previously collected forest health monitoring data. The canopy parameters are also compared with textural parameters from digital aerial mosaics. This study concludes that the classification of forest areas by using true colour data is not an easy task although the digital aerial mosaics are proved to be very accurate. The best classifications are still achieved with visual interpretation methods as the accuracies of the pixel-based and object-oriented supervised classification methods are not satisfying. According to the change detection of the land cover in the study areas, the area of indigenous woodland in both forests has decreased in 1955 2004. However in Ngangao, the overall woodland area has grown mainly because of plantations of exotic species. In general, the land cover of both study areas is more fragmented in 2004 than in 1955. Although the forest area has decreased, forests seem to have a more optimistic future than before. This is due to the increasing appreciation of the forest areas.

Mapping Road Infrastructure in Developing Countries Applying Remote Sensing and GIS - The Case of the Taita Hills, Kenya

Road transport and infrastructure has a fundamental meaning for the developing world. Poor quality and inadequate coverage of roads, lack of maintenance operations and outdated road maps continue to hinder economic and social development in the developing countries. This thesis focuses on studying the present state of road infrastructure and its mapping in the Taita Hills, south-east Kenya. The study is included as a part of the TAITA-project by the Department of Geography, University of Helsinki. The road infrastructure of the study area is studied by remote sensing and GIS based methodology. As the principal dataset, true colour airborne digital camera data from 2004, was used to generate an aerial image mosaic of the study area. Auxiliary data includes SPOT satellite imagery from 2003, field spectrometry data of road surfaces and relevant literature. Road infrastructure characteristics are interpreted from three test sites using pixel-based supervised classification, object-oriented supervised classifications and visual interpretation. Road infrastructure of the test sites is interpreted visually from a SPOT image. Road centrelines are then extracted from the object-oriented classification results with an automatic vectorisation process. The road infrastructure of the entire image mosaic is mapped by applying the most appropriate assessed data and techniques. The spectral characteristics and reflectance of various road surfaces are considered with the acquired field spectra and relevant literature. The results are compared with the experimented road mapping methods. This study concludes that classification and extraction of roads remains a difficult task, and that the accuracy of the results is inadequate regardless of the high spatial resolution of the image mosaic used in this thesis. Visual interpretation, out of all the experimented methods in this thesis is the most straightforward, accurate and valid technique for road mapping. Certain road surfaces have similar spectral characteristics and reflectance values with other land cover and land use. This has a great influence for digital analysis techniques in particular. Road mapping is made even more complicated by rich vegetation and tree canopy, clouds, shadows, low contrast between roads and surroundings and the width of narrow roads in relation to the spatial resolution of the imagery used. The results of this thesis may be applied to road infrastructure mapping in developing countries on a more general context, although with certain limits. In particular, unclassified rural roads require updated road mapping schemas to intensify road transport possibilities and to assist in the development of the developing world.

Mining Land Cover Information Using Multilayer Perceptron and Decision Tree from MODIS Data

Land cover (LC) changes play a major role in global as well as at regional scale patterns of the climate and biogeochemistry of the Earth system. LC information presents critical insights in understanding of Earth surface phenomena, particularly useful when obtained synoptically from remote sensing data. However, for developing countries and those with large geographical extent, regular LC mapping is prohibitive with data from commercial sensors (high cost factor) of limited spatial coverage (low temporal resolution and band swath). In this context, free MODIS data with good spectro-temporal resolution meet the purpose. LC mapping from these data has continuously evolved with advances in classification algorithms. This paper presents a comparative study of two robust data mining techniques, the multilayer perceptron (MLP) and decision tree (DT) on different products of MODIS data corresponding to Kolar district, Karnataka, India. The MODIS classified images when compared at three different spatial scales (at district level, taluk level and pixel level) shows that MLP based classification on minimum noise fraction components on MODIS 36 bands provide the most accurate LC mapping with 86% accuracy, while DT on MODIS 36 bands principal components leads to less accurate classification (69%).

A note on surface water waves for finite depth in the presence of an ice-cover

A class of I boundary value problems involving propagation of two-dimensional surface water waves, associated with water of uniform finite depth, against a plane vertical wave maker is investigated under the assumption that the surface is covered by a thin sheet of ice. It is assumed that the ice-cover behaves like a thin isotropic elastic plate. Then the problems under consideration lead to those of solving the two-dimensional Laplace equation in a semi-infinite strip, under Neumann boundary conditions on the vertical boundary as well as on one of the horizontal boundaries, representing the bottom of the fluid region, and a condition involving upto fifth order derivatives of the unknown function on the top horizontal ice-covered boundary, along with the two appropriate edge-conditions, at the ice-covered corner, ensuring the uniqueness of the solutions. The mixed boundary value problems are solved completely, by exploiting the regularity property of the Fourier cosine transform.

Contrained linear spectral unmixing technique for regional land cover mapping using MODIS data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up- to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat- TM/ETM+, IRS-1C/D LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (~ 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 m), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end- members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications.

Land Surface Temperature with Land Cover Dynamics:Multi-Resolution, Spatio-Temporal Data Analysis of Greater Bangalore

Bangalore is experiencing unprecedented urbanisation in recent times due to concentrated developmental activities with impetus on IT (Information Technology) and BT (Biotechnology) sectors. The concentrated developmental activities has resulted in the increase in population and consequent pressure on infrastructure, natural resources, ultimately giving rise to a plethora of serious challenges such as urban flooding, climate change, etc. One of the perceived impact at local levels is the increase in sensible heat flux from the land surface to the atmosphere, which is also referred as heat island effect. In this communication, we report the changes in land surface temperature (LST) with respect to land cover changes during 1973 to 2007. A novel technique combining the information from sub-pixel class proportions with information from classified image (using signatures of the respective classes collected from the ground) has been used to achieve more reliable classification. The analysis showed positive correlation with the increase in paved surfaces and LST. 466% increase in paved surfaces (buildings, roads, etc.) has lead to the increase in LST by about 2 ºC during the last 2 decades, confirming urban heat island phenomenon. LSTs’ were relatively lower (~ 4 to 7 ºC) at land uses such as vegetation (parks/forests) and water bodies which act as heat sinks.

Changes in seasonal snow cover in Hindu Kush-Himalayan region

The changes in seasonal snow covered area in the Hindu Kush-Himalayan (HKH) region have been examined using Moderate – resolution Imaging Spectroradiometer (MODIS) 8-day standard snow products. The average snow covered area of the HKH region based on satellite data from 2000 to 2010 is 0.76 million km2 which is 18.23% of the total geographical area of the region. The linear trend in annual snow cover from 2000 to 2010 is −1.25±1.13%. This is in consistent with earlier reported decline of the decade from 1990 to 2001. A similar trend for western, central and eastern HKH region is 8.55±1.70%, +1.66% ± 2.26% and 0.82±2.50%, respectively. The snow covered area in spring for HKH region indicates a declining trend (−1.04±0.97%). The amount of annual snowfall is correlated with annual seasonal snow cover for the western Himalaya, indicating that changes in snow cover are primarily due to interannual variations in circulation patterns. Snow cover trends over a decade were also found to vary across seasonally and the region. Snow cover trends for western HKH are positive for all seasons. In central HKH the trend is positive (+15.53±5.69%) in autumn and negative (−03.68±3.01) in winter. In eastern HKH the trend is positive in summer (+3.35±1.62%) and autumn (+7.74±5.84%). The eastern and western region of HKH has an increasing trend of 10% to 12%, while the central region has a declining trend of 12% to 14% in the decade between 2000 and 2010. Snow cover depletion curve plotted for the hydrological year 2000–2001 reveal peaks in the month of February with subsidiary peaks observed in November and December in all three regions of the HKH.