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An optimal data partitioning in parallel & distributed implementation of clustering algorithms is a necessary computation as it ensures independent task completion, fair distribution, less number of affected points and better & faster merging. Though partitioning using Kd Tree is being conventionally used in academia, it suffers from performance drenches and bias (non equal distribution) as dimensionality of data increases and hence is not suitable for practical use in industry where dimensionality can be of order of 100s to 1000s. To address these issues we propose two new partitioning techniques using existing mathematical models & study their feasibility, performance (bias and partitioning speed) & possible variants in choosing initial seeds. First method uses an n dimensional hashed grid based approach which is based on mapping the points in space to a set of cubes which hashes the points. Second method uses a tree of voronoi planes where each plane corresponds to a partition. We found that grid based approach was computationally impractical, while using a tree of voronoi planes (using scalable K-Means++ initial seeds) drastically outperformed the Kd-tree tree method as dimensionality increased.
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We also consider two string (1D data) processing problems, regarding an optimal encoding method and the computation of the number of occurrences of a substring within a string generated by a grammar. The algorithms have been thoroughly analyzed from a theoretical point of view and some of them have also been evaluated experimentally.
In this paper, we study the single-source shortest-path (SSSP) problem with positive edge weights, which is a notoriously hard problem in the parallel context. In practice, the $Delta$-stepping algorithm proposed by Meyer and Sanders has been widely adopted. However, $Delta$-stepping has no known worst-case bounds for general graphs. The performance of $Delta$-stepping also highly relies on the parameter $Delta$. There have also been lots of algorithms with theoretical bounds, such as Radius-stepping, but they either have no implementations available or are much slower than $Delta$-stepping in practice. We propose a stepping algorithm framework that generalizes existing algorithms such as $Delta$-stepping and Radius-stepping. The framework allows for similar analysis and implementations of all stepping algorithms. We also propose a new ADT, lazy-batched priority queue (LaB-PQ), that abstracts the semantics of the priority queue needed by the stepping algorithms. We provide two data structures for LaB-PQ, focusing on theoretical and practical efficiency, respectively. Based on the new framework and LaB-PQ, we show two new stepping algorithms, $rho$-stepping and $Delta^*$-stepping, that are simple, with non-trivial worst-case bounds, and fast in practice. The stepping algorithm framework also provides almost identical implementations for three algorithms: Bellman-Ford, $Delta^*$-stepping, and $rho$-stepping. We compare our code with four state-of-the-art implementations. On five social and web graphs, $rho$-stepping is 1.3--2.5x faster than all the existing implementations. On two road graphs, our $Delta^*$-stepping is at least 14% faster than existing implementations, while $rho$-stepping is also competitive. The almost identical implementations for stepping algorithms also allow for in-depth analyses and comparisons among the stepping algorithms in practice.
We propose a parallel graph-based data clustering algorithm using CUDA GPU, based on exact clustering of the minimum spanning tree in terms of a minimum isoperimetric criteria. We also provide a comparative performance analysis of our algorithm with other related ones which demonstrates the general superiority of this parallel algorithm over other competing algorithms in terms of accuracy and speed.
In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read performance being close to that of random access memory but writes being significantly more expensive in terms of energy and latency. We design algorithms for planar Delaunay triangulation, $k$-d trees, and static and dynamic augmented trees. Our algorithms are designed in the recently introduced Asymmetric Nested-Parallel Model, which captures the parallel setting in which there is a small symmetric memory where reads and writes are unit cost as well as a large asymmetric memory where writes are $omega$ times more expensive than reads. In designing these algorithms, we introduce several techniques for obtaining write-efficiency, including DAG tracing, prefix doubling, reconstruction-based rebalancing and $alpha$-labeling, which we believe will be useful for designing other parallel write-efficient algorithms.
Autonomous Driving is now the promising future of transportation. As one basis for autonomous driving, High Definition Map (HD map) provides high-precision descriptions of the environment, therefore it enables more accurate perception and localization while improving the efficiency of path planning. However, an extremely large amount of map data needs to be transmitted during driving, thus posing great challenge for real-time and safety requirements for autonomous driving. To this end, we first demonstrate how the existing data distribution mechanism can support HD map services. Furthermore, considering the constraints of vehicle power, vehicle speed, base station bandwidth, etc., we propose a HD map data distribution mechanism on top of Vehicle-to-Infrastructure (V2I) data transmission. By this mechanism, the map provision task is allocated to the selected RSU nodes and transmits proportionate HD map data cooperatively. Their works on map data loading aims to provide in-time HD map data service with optimized in-vehicle energy consumption. Finally, we model the selection of RSU nodes into a partial knapsack problem and propose a greedy strategy-based data transmission algorithm. Experimental results confirm that within limited energy consumption, the proposed mechanism can ensure HD map data service by coordinating multiple RSUs with the shortest data transmission time.