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

Multidimensional Range Queries on Modern Hardware

Range queries over multidimensional data are an important part of database workloads in many applications. Their execution may be accelerated by using multidimensional index structures (MDIS), such as kd-trees or R-trees. As for most index structures, the usefulness of this approach depends on the selectivity of the queries, and common wisdom told that a simple scan beats MDIS for queries accessing more than 15%-20% of a dataset. However, this wisdom is largely based on evaluations that are almost two decades old, performed on data being held on disks, applying IO-optimized data structures, and using single-core systems. The question is whether this rule of thumb still holds when multidimensional range queries (MDRQ) are performed on modern architectures with large main memories holding all data, multi-core CPUs and data-parallel instruction sets. In this paper, we study the question whether and how much modern hardware influences the performance ratio between index structures and scans for MDRQ. To this end, we conservatively adapted three popular MDIS, namely the R*-tree, the kd-tree, and the VA-file, to exploit features of modern servers and compared their performance to different flavors of parallel scans using multiple (synthetic and real-world) analytical workloads over multiple (synthetic and real-world) datasets of varying size, dimensionality, and skew. We find that all approaches benefit considerably from using main memory and parallelization, yet to varying degrees. Our evaluation indicates that, on current machines, scanning should be favored over parallel versions of classical MDIS even for very selective queries

Experiences with Mesh-like computations using Prediction Binary Trees

In this paper we aim at exploiting the temporal coherence among successive phases of a computation, in order to implement a load-balancing technique in mesh-like computations to be mapped on a cluster of processors. A key concept, on which the load balancing schema is built on, is the use of a Predictor component that is in charge of providing an estimation of the unbalancing between successive phases. By using this information, our method partitions the computation in balanced tasks through the Prediction Binary Tree (PBT). At each new phase, current PBT is updated by using previous phase computing time for each task as next phase's cost estimate. The PBT is designed so that it balances the load across the tasks as well as reduces {\em dependency} among processors for higher performances. Reducing dependency is obtained by using rectangular tiles of the mesh, of almost-square shape (i. e. one dimension is at most twice the other). By reducing dependency, one can reduce inter-processors communication or exploit local dependencies among tasks (such as data locality). Furthermore, we also provide two heuristics which take advantage of data-locality. Our strategy has been assessed on a significant problem, Parallel Ray Tracing. Our implementation shows a good scalability, and improves performance in both cheaper commodity cluster and high performance clusters with low latency networks. We report different measurements showing that tasks granularity is a key point for the performances of our decomposition/mapping strategy

A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our existing single-GPU hierarchical matrix library hmglib such that it is able to scale on many GPUs and such that it can be coupled to arbitrary application codes. Using a model GPU implementation of a boundary element method (BEM) solver, we are able to achieve more than 67 percent relative parallel speed-up going from 128 to 1024 GPUs for a model geometry test case with 1.5 million unknowns and a real-world geometry test case with almost 1.2 million unknowns. On 1024 GPUs of the cluster Titan, it takes less than 6 minutes to solve the 1.5 million unknowns problem, with 5.7 minutes for the setup phase and 20 seconds for the iterative solver. To the best of the authors' knowledge, we here discuss the first fully GPU-based distributed-memory parallel hierarchical matrix Open Source library using the traditional H-matrix format and adaptive cross approximation with an application to BEM problems

A multi-resource load balancing algorithm for cloud cache systems

With the advent of cloud computing model, distributed caches have become the cornerstone for building scalable applications. Popular systems like Facebook [1] or Twitter use Memcached [5], a highly scalable distributed object cache, to speed up applications by avoiding database accesses. Distributed object caches assign objects to cache instances based on a hashing function, and objects are not moved from a cache instance to another unless more instances are added to the cache and objects are redistributed. This may lead to situations where some cache instances are overloaded when some of the objects they store are frequently accessed, while other cache instances are less frequently used. In this paper we propose a multi-resource load balancing algorithm for distributed cache systems. The algorithm aims at balancing both CPU and Memory resources among cache instances by redistributing stored data. Considering the possible conflict of balancing multiple resources at the same time, we give CPU and Memory resources weighted priorities based on the runtime load distributions. A scarcer resource is given a higher weight than a less scarce resource when load balancing. The system imbalance degree is evaluated based on monitoring information, and the utility load of a node, a unit for resource consumption. Besides, since continuous rebalance of the system may affect the QoS of applications utilizing the cache system, our data selection policy ensures that each data migration minimizes the system imbalance degree and hence, the total reconfiguration cost can be minimized. An extensive simulation is conducted to compare our policy with other policies. Our policy shows a significant improvement in time efficiency and decrease in reconfiguration cost