Dynamic load balancing in parallel KD-tree k-means

One among the most influential and popular data mining methods is the k-Means algorithm for cluster analysis. Techniques for improving the efficiency of k-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting geometrical constraints and an efficient data structure, notably a multidimensional binary search tree (KD-Tree). These techniques allow to reduce the number of distance computations the algorithm performs at each iteration. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient k-Means variants in parallel computing environments. In this work, we provide a parallel formulation of the KD-Tree based k-Means algorithm for distributed memory systems and address its load balancing issue. Three solutions have been developed and tested. Two approaches are based on a static partitioning of the data set and a third solution incorporates a dynamic load balancing policy

Enumerating Maximal Bicliques from a Large Graph using MapReduce

We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the MapReduce platform, and an experimental evaluation using Hadoop MapReduce. Our algorithm is based on clustering the input graph into smaller sized subgraphs, followed by processing different subgraphs in parallel. Our algorithm uses two ideas that enable it to scale to large graphs: (1) the redundancy in work between different subgraph explorations is minimized through a careful pruning of the search space, and (2) the load on different reducers is balanced through the use of an appropriate total order among the vertices. Our evaluation shows that the algorithm scales to large graphs with millions of edges and tens of mil- lions of maximal bicliques. To our knowledge, this is the first work on maximal biclique enumeration for graphs of this scale.Comment: A preliminary version of the paper was accepted at the Proceedings of the 3rd IEEE International Congress on Big Data 201

Window-based Streaming Graph Partitioning Algorithm

In the recent years, the scale of graph datasets has increased to such a degree that a single machine is not capable of efficiently processing large graphs. Thereby, efficient graph partitioning is necessary for those large graph applications. Traditional graph partitioning generally loads the whole graph data into the memory before performing partitioning; this is not only a time consuming task but it also creates memory bottlenecks. These issues of memory limitation and enormous time complexity can be resolved using stream-based graph partitioning. A streaming graph partitioning algorithm reads vertices once and assigns that vertex to a partition accordingly. This is also called an one-pass algorithm. This paper proposes an efficient window-based streaming graph partitioning algorithm called WStream. The WStream algorithm is an edge-cut partitioning algorithm, which distributes a vertex among the partitions. Our results suggest that the WStream algorithm is able to partition large graph data efficiently while keeping the load balanced across different partitions, and communication to a minimum. Evaluation results with real workloads also prove the effectiveness of our proposed algorithm, and it achieves a significant reduction in load imbalance and edge-cut with different ranges of dataset

Adaptive Partitioning for Large-Scale Dynamic Graphs

Abstract—In the last years, large-scale graph processing has gained increasing attention, with most recent systems placing particular emphasis on latency. One possible technique to improve runtime performance in a distributed graph processing system is to reduce network communication. The most notable way to achieve this goal is to partition the graph by minimizing the num-ber of edges that connect vertices assigned to different machines, while keeping the load balanced. However, real-world graphs are highly dynamic, with vertices and edges being constantly added and removed. Carefully updating the partitioning of the graph to reflect these changes is necessary to avoid the introduction of an extensive number of cut edges, which would gradually worsen computation performance. In this paper we show that performance degradation in dynamic graph processing systems can be avoided by adapting continuously the graph partitions as the graph changes. We present a novel highly scalable adaptive partitioning strategy, and show a number of refinements that make it work under the constraints of a large-scale distributed system. The partitioning strategy is based on iterative vertex migrations, relying only on local information. We have implemented the technique in a graph processing system, and we show through three real-world scenarios how adapting graph partitioning reduces execution time by over 50 % when compared to commonly used hash-partitioning. I

Dynamically Adjusting the Mining Capacity in Cryptocurrency with Binary Blockchain

Many cryptocurrencies rely on Blockchain for its operation. Blockchain serves as a public ledger where all the completed transactions can be looked up. To place transactions in the Blockchain, a mining operation must be performed. However, due to a limited mining capacity, the transaction confirmation time is increasing. To mitigate this problem many ideas have been proposed, but they all come with own challenges. We propose a novel parallel mining method that can adjust the mining capacity dynamically depending on the congestion level. It does not require an increase in the block size or a reduction of the block confirmation time. The proposed scheme can increase the number of parallel blockchains when the mining congestion is experienced, which is especially effective under DDoS attack situation. We describe how and when the Blockchain is split or merged, how to solve the imbalanced mining problem, and how to adjust the difficulty levels and rewards. We then show the simulation results comparing the performance of binary blockchain and the traditional single blockchain