Big data refers to information which cannot be processed and analyzed using traditional approaches and tools, due to 4 V's - sheer Volume, Velocity at which data is received and processed, and data Variety and Veracity. Today massive volumes of data originate in domains such as geospatial analysis, biological and social networks, etc. Hence, scalable algorithms for effcient processing of this massive data is a signicant challenge in the field of computer science. One way to achieve such effcient and scalable algorithms is by using shared & distributed memory parallel programming models. In this thesis, we present a variety of such algorithms to solve problems in various above mentioned domains. We solve five problems that fall into two categories. The first group of problems deals with the issue of community detection. Detecting communities in real world networks is of great importance because they consist of patterns that can be viewed as independent components, each of which has distinct features and can be detected based upon network structure. For example, communities in social networks can help target users for marketing purposes, provide user recommendations to connect with and join communities or forums, etc. We develop a novel sequential algorithm to accurately detect community structures in biological protein-protein interaction networks, where a community corresponds with a functional module of proteins. Generally, such sequential algorithms are computationally expensive, which makes them impractical to use for large real world networks. To address this limitation, we develop a new highly scalable Symmetric Multiprocessing (SMP) based parallel algorithm to detect high quality communities in large subsections of social networks like Facebook and Amazon. Due to the SMP architecture, however, our algorithm cannot process networks whose size is greater than the size of the RAM of a single machine. With the increasing size of social networks, community detection has become even more difficult, since network size can reach up to hundreds of millions of vertices and edges. Processing such massive networks requires several hundred gigabytes of RAM, which is only possible by adopting distributed infrastructure. To address this, we develop a novel hybrid (shared + distributed memory) parallel algorithm to efficiently detect high quality communities in massive Twitter and .uk domain networks. The second group of problems deals with the issue of effciently processing spatial Light Detection and Ranging (LiDAR) data. LiDAR data is widely used in forest and agricultural crop studies, landscape classification, 3D urban modeling, etc. Technological advancements in building LiDAR sensors have enabled highly accurate and dense LiDAR point clouds resulting in massive data volumes, which pose computing issues with processing and storage. We develop the first published landscape driven data reduction algorithm, which uses the slope-map of the terrain as a filter to reduce the data without sacrificing its accuracy. Our algorithm is highly scalable and adopts shared memory based parallel architecture. We also develop a parallel interpolation technique that is used to generate highly accurate continuous terrains, i.e. Digital Elevation Models (DEMs), from discrete LiDAR point clouds.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.