Assigning a large number of independent tasks to heterogeneous processors is a fundamental problem in modern computing, with applications in many domains such as cloud services, web crawling, and AI training. Exact and matheuristic approaches deliver high-quality assignments but incur superlinear or even exponential runtime costs, making them impractical, especially on large problem instances. Conversely, lightweight heuristics run efficiently at scale but often produce assignments with much lower quality. To address this issue, we present the first multilevel framework for the independent task assignment problem that maintains an end-to-end linear runtime bound of O ( K N ) , where K × N is the size of the expected-time-to-compute matrix, with K and N respectively representing the number of processors and tasks. We propose (i) novel high-quality coarsening metrics that numerically define task characteristics and similarity; (ii) an efficient and effective matching algorithm that incorporates these metrics while maintaining linear time complexity with respect to the input size; (iii) an initial solution scheme that generates base solutions using complementary heuristics, which are disjointly projected back through the uncoarsening levels; (iv) an effective and efficient uncoarsening algorithm that iteratively improves assignment quality with different refinement algorithms. Extensive experimental evaluations involving hundreds of millions of tasks demonstrate that our algorithm achieves significantly higher quality and runs faster than known high-quality heuristics, making it a practical choice for the problem instances at high scale.

We propose an algorithm to efficiently perform latency-bound communication scenarios that consist of many small messages. In these parallel scenarios, processes typically pass around a lot of small-sized messages of a few KBs of size. Performing communication operations with P2P MPI routines or collective MPI routines (including neighborhood collectives) in such scenarios may not always yield the optimal results and may not resolve the latency bottleneck. To this end, we develop a regular structure called virtual process topology (VPT) on which the messages can be communicated in a structured and controlled manner. Using parameters of this topology, one can tune the rate of aggression in tackling the latency costs. We demonstrate that our communication algorithm is preferable to MPI P2P and collective routines for latency-bound communication and it can easily be adapted only by replacing calls to MPI routines in a parallel application. We show how to adapt existing topology-aware mapping heuristics to address the volume overhead due to communicating messages on the VPT. Moreover, we propose a novel swap-based mapping heuristic to address this overhead by optimizing the maximum volume handled by a process. Experiments on synthetic communication graphs as well as real-world applications such as parallel Canonical Polyadic sparse tensor decomposition and parallel sparse matrix-dense matrix multiplication show that our approach is a powerful way of overcoming the bottlenecks posed by sparse and latency-bound irregular communication.

Distributed asynchronous stochastic gradient descent (ASGD) algorithms that approximate low-rank matrix factorizations for collaborative filtering perform one or more synchronizations per epoch where staleness is reduced with more synchronizations. However, high number of synchronizations would prohibit the scalability of the algorithm. We propose a parallel ASGD algorithm,$\eta$-PASGD, for efficiently handling$\eta$synchronizations per epoch in a scalable fashion. The proposed algorithm puts an upper limit of$K$on$\eta$, for a$K$-processor system, such that performing$\eta =K$synchronizations per epoch would eliminate the staleness completely. The rating data used in collaborative filtering are usually represented as sparse matrices. The sparsity allows for reduction in the staleness and communication overhead combinatorially via intelligently distributing the data to processors. We analyze the staleness and the total volume incurred during an epoch of$\eta$-PASGD. Following this analysis, we propose a hypergraph partitioning model to encapsulate reducing staleness and volume while minimizing the maximum number of synchronizations required for a stale-free SGD. This encapsulation is achieved with a novel cutsize metric that is realized via a new recursive-bipartitioning-based algorithm. Experiments on up to 512 processors show the importance of the proposed partitioning method in improving staleness, volume, RMSE and parallel runtime.

Stratified SGD (SSGD) is the primary approach for achieving serializable parallel SGD for matrix completion. State-of-the-art parallelizations of SSGD fail to scale due to large communication overhead. During an SGD epoch, these methods send data proportional to one of the dimensions of the rating matrix. We propose a framework for scalable SSGD through significantly reducing the communication overhead via exchanging point-to-point messages utilizing the sparsity of the rating matrix. We provide formulas to represent the essential communication for correctly performing parallel SSGD and we propose a dynamic programming algorithm for efficiently computing them to establish the point-to-point message schedules. This scheme, however, significantly increases the number of messages sent by a processor per epoch from$\mathcal {O}(K)$to$\mathcal {O}(K^{2})$for a$K$-processor system which might limit the scalability. To remedy this, we propose a Hold-and-Combine strategy to limit the upper-bound on the number of messages sent per processor to$\mathcal {O}(K\lg \!K)$. We also propose a hypergraph partitioning model that correctly encapsulates reducing the communication volume. Experimental results show that the framework successfully achieves a scalable distributed SSGD through significantly reducing the communication overhead. Our code is publicly available at: github.com/nfabubaker/CESSGD

Latency overhead in distributed-memory parallel CPD-ALS scales with the number of processors, limiting the scalability of computing CPD of large irregularly sparse tensors. This overhead comes in the form of sparse reduce and expand operations performed on factor-matrix rows via point-to-point messages. We propose to hide the latency overhead through embedding all of the point-to-point messages incurred by the sparse reduce and expand into dense collective operations which already exist in the CPD-ALS. The conventional parallel CPD-ALS algorithm is not amenable for embedding so we propose a computation/communication rearrangement to enable the embedding. We embed the sparse expand and reduce into a hypercube-based ALL-REDUCE operation to limit the latency overhead to O(log K) for a K-processor system. The embedding comes with the cost of increased bandwidth overhead due to the multi-hop routing of factor-matrix rows during the embedded-ALL-REDUCE. We propose an embedding scheme that takes advantage of the expand/reduce properties to reduce this overhead. Furthermore, we propose a novel recursive bipartitioning framework that enables simultaneous hypergraph partitioning and subhypergraph-to-subhypercube mapping to achieve subtensor-to-processor assignment with the objective of reducing the bandwidth overhead during the embedded-ALL-REDUCE. We also propose a bin-packing-based algorithm for factor-matrix row to processor assignment aiming at reducing processors maximum send and receive volumes during the embedded-ALL-REDUCE. Experiments on up to 4096 processors show that the proposed framework scales significantly better than the state-of-the-art point-to-point method.

MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. Parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.

The focus of this article is efficient parallelization of the canonical polyadic decomposition algorithm utilizing the alternating least squares method for sparse tensors on distributed-memory architectures. We propose a hypergraph model for general medium-grain partitioning which does not enforce any topological constraint on the partitioning. The proposed model is based on splitting the given tensor into nonzero-disjoint component tensors. Then a mode-dependent coarse-grain hypergraph is constructed for each component tensor. A net amalgamation operation is proposed to form a composite medium-grain hypergraph from these mode-dependent coarse-grain hypergraphs to correctly encapsulate the minimization of the communication volume. We propose a heuristic which splits the nonzeros of dense slices to obtain sparse slices in component tensors. So we partially attain slice coherency at (sub)slice level since partitioning is performed on (sub)slices instead of individual nonzeros. We also utilize the well-known recursive-bipartitioning framework to improve the quality of the splitting heuristic. Finally, we propose a medium-grain tripartite graph model with the aim of a faster partitioning at the expense of increasing the total communication volume. Parallel experiments conducted on 10 real-world tensors on up to 1024 processors confirm the validity of the proposed hypergraph and graph models.

The focus is distributed-memory parallelization of sparse-general-matrix-multiplication (SpGEMM). Parallel SpGEMM algorithms are classified under one-dimensional (1D), 2D, and 3D categories denoting the number of dimensions by which the 3D sparse workcube representing the iteration space of SpGEMM is partitioned. Recently proposed successful 2D- and 3D-parallel SpGEMM algorithms benefit from upper bounds on communication overheads enforced by 2D and 3D cartesian partitioning of the workcube on 2D and 3D virtual processor grids, respectively. However, these methods are based on random cartesian partitioning and do not utilize sparsity patterns of SpGEMM instances for reducing the communication overheads. We propose hypergraph models for 2D and 3D cartesian partitioning of the workcube for further reducing the communication overheads of these 2D- and 3D- parallel SpGEMM algorithms. The proposed models utilize two- and three-phase partitioning that exploit multi-constraint hypergraph partitioning formulations. Extensive experimentation performed on 20 SpGEMM instances by using upto 900 processors demonstrate that proposed partitioning models significantly improve the scalability of 2D and 3D algorithms. For example, in 2D-parallel SpGEMM algorithm on 900 processors, the proposed partitioning model respectively achieves 85 and 42 percent decrease in total volume and total number of messages, leading to 1.63 times higher speedup compared to random partitioning, on average.

Communication hypergraph model was proposed in a two-phase setting for encapsulating multiple communication cost metrics (bandwidth and latency), which are proven to be important in parallelizing irregular applications. In the first phase, computational-task-to-processor assignment is performed with the objective of minimizing total volume while maintaining computational load balance. In the second phase, communication-task-to-processor assignment is performed with the objective of minimizing total number of messages while maintaining communication-volume balance. The reduce-communication hypergraph model suffers from failing to correctly encapsulate send-volume balancing. We propose a novel vertex weighting scheme that enables part weights to correctly encode send-volume loads of processors for send-volume balancing. The model also suffers from increasing the total communication volume during partitioning. To decrease this increase, we propose a method that utilizes the recursive bipartitioning framework and refines each bipartition by vertex swaps. For performance evaluation, we consider column-parallel SpMV, which is one of the most widely known applications in which the reduce-task assignment problem arises. Extensive experiments on 313 matrices show that, compared to the existing model, the proposed models achieve considerable improvements in all communication cost metrics. These improvements lead to an average decrease of 30 percent in parallel SpMV time on 512 processors for 70 matrices with high irregularity.

This work tackles the communication challenges posed by the latency-bound applications with irregular communication patterns, i.e., applications with high average and/or maximum message counts. We propose a novel algorithm for reorganizing a given set of irregular point-to-point messages with the objective of reducing total latency cost at the expense of increased volume. We organize processes into a virtual process topology inspired by the k-ary n-cube networks and regularize irregular messages by imposing regular communication pattern(s) onto them. Exploiting this process topology, we propose a flexible store-and-forward algorithm to control the trade-off between latency and volume. Our approach is able to reduce the communication time of sparse-matrix multiplication with latency-bound instances drastically: up to 22.6× for 16K processes on a 3D Torus network and up to 7.2× for 4K processes on a Dragonfly network, with its performance getting better with increasing number of processes.

There exist graph/hypergraph partitioning-based row/column reordering methods for encoding either spatial or temporal locality for sparse matrix-vector multiplication (SpMV) operations. Spatial and temporal hypergraph models in these methods are extended to encapsulate both spatial and temporal localities based on cut/uncut net categorization obtained from vertex partitioning. These extensions of spatial and temporal hypergraph models encode the spatial locality primarily and the temporal locality secondarily, and vice-versa, respectively. However, the literature lacks models that simultaneously encode both spatial and temporal localities utilizing only vertex partitioning for further improving the performance of SpMV on shared-memory architectures. In order to fill this gap, we propose a novel spatiotemporal hypergraph model that leads to a one-phase spatiotemporal reordering method which encodes both types of locality simultaneously. We also propose a framework for spatiotemporal methods which encodes both types of locality in two dependent phases and two separate phases. The validity of the proposed spatiotemporal models and methods are tested on a wide range of sparse matrices and the experiments are performed on both a 60-core Intel Xeon Phi processor and a Xeon processor. Results show the validity of the methods via almost doubling the Gflop/s performance through enhancing data locality in parallel SpMV operations.

Graph partitioning is an essential task for scalable data management and analysis. The current partitioning methods utilize the structure of the graph, and the query log if available. Some queries performed on the database may trigger further operations. For example, the query workload of a social network application may contain re-sharing operations in the form of cascades. It is beneficial to include the potential cascades in the graph partitioning objectives. In this paper, we introduce the problem of cascade-aware graph partitioning that aims to minimize the overall cost of communication among parts/servers during cascade processes. We develop a randomized solution that estimates the underlying cascades, and use it as an input for partitioning of large-scale graphs. Experiments on 17 real social networks demonstrate the effectiveness of the proposed solution in terms of the partitioning objectives.

Tensor decomposition is widely used in the analysis of multi-dimensional data. The canonical polyadic decomposition (CPD) is one of the most popular decomposition methods and commonly found by the CPD-ALS algorithm. High computational and memory costs of CPD-ALS necessitate the use of a distributed-memory-parallel algorithm for efficiency. The medium-grain CPD-ALS algorithm, which adopts multi-dimensional cartesian tensor partitioning, is one of the most successful distributed CPD-ALS algorithms for sparse tensors. This is because cartesian partitioning imposes nice upper bounds on communication overheads. However, this model does not utilize the sparsity pattern of the tensor to reduce the total communication volume. The objective of this work is to fill this literature gap. We propose a novel hypergraph-partitioning model, CartHP, whose partitioning objective correctly encapsulates the minimization of total communication volume of multi-dimensional cartesian tensor partitioning. Experiments on twelve real-world tensors using up to 1024 processors validate the effectiveness of the proposed CartHP model. Compared to the baseline medium-grain model, CartHP achieves average reductions of 52, 43 and 24 percent in total communication volume, communication time and overall runtime of CPD-ALS, respectively.

Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for obtaining the minimum 2-norm solution of an underdetermined system of equations. The proposed algorithm is based on the Balance scheme, which was originally developed for the parallel solution of banded linear systems. The proposed scheme assumes a generalized banded form where the coefficient matrix has column overlapped block structure in which the blocks could be dense or sparse. In this article, we implement the more general sparse case. The blocks can be handled independently by any existing sequential or parallel QR factorization library. A smaller reduced system is formed and solved before obtaining the minimum norm solution of the original system in parallel. We experimentally compare and confirm the error bound of the proposed method against the QR factorization based techniques by using true single-precision arithmetic. We implement the proposed algorithm by using the message passing paradigm. We demonstrate numerical effectiveness as well as parallel scalability of the proposed algorithm on both shared and distributed memory architectures for solving various types of problems.

Exploiting spatial and temporal localities is investigated for efficient row-by-row parallelization of general sparse matrix-matrix multiplication (SpGEMM) operation of the form C=AB on many-core architectures. Hypergraph and bipartite graph models are proposed for 1D rowwise partitioning of matrix A to evenly partition the work across threads with the objective of reducing the number of B-matrix words to be transferred from the memory and between different caches. A hypergraph model is proposed for B-matrix column reordering to exploit spatial locality in accessing entries of thread-private temporary arrays, which are used to accumulate results for C-matrix rows. A similarity graph model is proposed for B-matrix row reordering to increase temporal reuse of these accumulation array entries. The proposed models and methods are tested on a wide range of sparse matrices from real applications and the experiments were carried on a 60-core Intel Xeon Phi processor, as well as a two-socket Xeon processor. Results show the validity of the models and methods proposed for enhancing the locality in parallel SpGEMM operations.

Intelligent partitioning models are commonly used for efficient parallelization of irregular applications on distributed systems. These models usually aim to minimize a single communication cost metric, which is either related to communication volume or message count. However, both volume- and message-related metrics should be taken into account during partitioning for a more efficient parallelization. There are only a few works that consider both of them and they usually address each in separate phases of a two-phase approach. In this work, we propose a recursive hypergraph bipartitioning framework that reduces the total volume and total message count in a single phase. In this framework, the standard hypergraph models, nets of which already capture the bandwidth cost, are augmented with message nets. The message nets encode the message count so that minimizing conventional cutsize captures the minimization of bandwidth and latency costs together. Our model provides a more accurate representation of the overall communication cost by incorporating both the bandwidth and the latency components into the partitioning objective. The use of the widely-adopted successful recursive bipartitioning framework provides the flexibility of using any existing hypergraph partitioner. The experiments on instances from different domains show that our model on the average achieves up to 52 percent reduction in total message count and hence results in 29 percent reduction in parallel running time compared to the model that considers only the total volume.

We propose a comprehensive and generic framework to minimize multiple and different volume-based communication cost metrics for sparse matrix dense matrix multiplication (SpMM). SpMM is an important kernel that finds application in computational linear algebra and big data analytics. On distributed memory systems, this kernel is usually characterized with its high communication volume requirements. Our approach targets irregularly sparse matrices and is based on both graph and hypergraph partitioning models that rely on the widely adopted recursive bipartitioning paradigm. The proposed models are lightweight, portable (can be realized using any graph and hypergraph partitioning tool) and can simultaneously optimize different cost metrics besides total volume, such as maximum send/receive volume, maximum sum of send and receive volumes, etc., in a single partitioning phase. They allow one to define and optimize as many custom volume-based metrics as desired through a flexible formulation. The experiments on a wide range of about thousand matrices show that the proposed models drastically reduce the maximum communication volume compared to the standard partitioning models that only address the minimization of total volume. The improvements obtained on volume-based partition quality metrics using our models are validated with parallel SpMM as well as parallel multi-source BFS experiments on two large-scale systems. For parallel SpMM, compared to the standard partitioning models, our graph and hypergraph partitioning models respectively achieve reductions of 14% and 22% in runtime, on average. Compared to the state-of-the-art partitioner UMPa, our graph model is overall 14.5 × faster and achieves an average improvement of 19% in the partition quality on instances that are bounded by maximum volume. For parallel BFS, we show on graphs with more than a billion edges that the scalability can significantly be improved with our models compared to a recently proposed two-dimensional partitioning model.

Sparse matrix-vector and matrix-transpose-vector multiplication (SpMMTV) repeatedly performed as z←ATxand y← A z (or y A w) for the same sparse matrix A is a kernel operation widely used in various iterative solvers. One important optimization for serial SpMMTV is reusing A-matrix nonzeros, which halves the memory bandwidth requirement. However, thread-level parallelization of SpMMTV that reuses A-matrix nonzeros necessitates concurrent writes to the same output-vector entries. These concurrent writes can be handled in two ways: via atomic updates or thread-local temporary output vectors that will undergo a reduction operation, both of which are not efficient or scalable on processors with many cores and complicated cache-coherency protocols. In this work, we identify five quality criteria for efficient and scalable thread-level parallelization of SpMMTV that utilizes one-dimensional (1D) matrix partitioning. We also propose two locality-aware 1D partitioning methods, which achieve reusing A-matrix nonzeros and intermediate z-vector entries; exploiting locality in accessing x-, y-, and z-vector entries; and reducing the number of concurrent writes to the same output-vector entries. These two methods utilize rowwise and columnwise singly bordered block-diagonal (SB) forms of A. We evaluate the validity of our methods on a wide range of sparse matrices. Experiments on the 60-core cache-coherent Intel Xeon Phi processor show the validity of the identified quality criteria and the validity of the proposed methods in practice. The results also show that the performance improvement from reusing A-matrix nonzeros compensates for the overhead of concurrent writes through the proposed SB-based methods.

In parallel linear iterative solvers, sparse matrix vector multiplication (SpMxV) incurs irregular point-to-point (P2P) communications, whereas inner product computations incur regular collective communications. These P2P communications cause an additional synchronization point with relatively high message latency costs due to small message sizes. In these solvers, each SpMxV is usually followed by an inner product computation that involves the output vector of SpMxV. Here, we exploit this property to propose a novel parallelization method that avoids the latency costs and synchronization overhead of P2P communications. Our method involves a computational and a communication rearrangement scheme. The computational rearrangement provides an alternative method for forming input vector of SpMxV and allows P2P and collective communications to be performed in a single phase. The communication rearrangement realizes this opportunity by embedding P2P communications into global collective communication operations. The proposed method grants a certain value on the maximum number of messages communicated regardless of the sparsity pattern of the matrix. The downside, however, is the increased message volume and the negligible redundant computation. We favor reducing the message latency costs at the expense of increasing message volume. Yet, we propose two iterative-improvementbased heuristics to alleviate the increase in the volume through one-to-one task-to-processor mapping. Our experiments on two supercomputers, Cray XE6 and IBM BlueGene/Q, up to 2,048 processors show that the proposed parallelization method exhibits superior scalable performance compared to the conventional parallelization method.

Replication is a widely-used technique in information retrieval and database systems for providing fault tolerance and reducing parallelization and processing costs. Combinatorial models based on hypergraph partitioning are proposed for various problems arising in information retrieval and database systems. We consider the possibility of using vertex replication to improve the quality of hypergraph partitioning. In this study, we focus on the constrained min-cut replication (CMCR) problem, where we are initially given a maximum replication capacity and a K-way hypergraph partition with an initial imbalance ratio. The objective in the CMCR problem is finding the optimal vertex replication sets for each part of the given partition such that the initial cut size of the partition is minimized, where the initial imbalance is either preserved or reduced under the given replication capacity constraint. In this study, we present a complexity analysis of the CMCR problem and propose a model based on a unique blend of coarsening and integer linear programming (ILP) schemes. This coarsening algorithm is derived from a novel utilization of the Dulmage-Mendelsohn decomposition. Experiments show that the ILP formulation coupled with the Dulmage-Mendelsohn decomposition-based coarsening provides high quality results in practical execution times for reducing the cut size of a given K-way hypergraph partition.

Most frequent and expensive queries in social networks involve multi-user operations such as requesting the latest tweets or news-feeds of friends. The performance of such queries are heavily dependent on the data partitioning and replication methodologies adopted by the underlying systems. Existing solutions for data distribution in these systems involve hashor graph-based approaches that ignore the multi-way relations among data. In this work, we propose a novel data partitioning and selective replication method that utilizes the temporal information in prior workloads to predict future query patterns. Our method utilizes the social network structure and the temporality of the interactions among its users to construct a hypergraph that correctly models multi-user operations. It then performs simultaneous partitioning and replication of this hypergraph to reduce the query span while respecting load balance and I/O load constraints under replication. To test our model, we enhance the Cassandra NoSQL system to support selective replication and we implement a social network application (a Twitter clone) utilizing our enhanced Cassandra. We conduct experiments on a cloud computing environment (Amazon EC2) to test the developed systems. Comparison of the proposed method with hash- and enhanced graph-based schemes indicate that it significantly improves latency and throughput.

MinMin, MaxMin, and Sufferage are constructive heuristics that are widely and successfully used in assigning independent tasks to processors in heterogeneous computing systems. All three heuristics are known to run in O(KN2) time in assigning N tasks to K processors. In this paper, we propose an algorithmic improvement that asymptotically decreases the running time complexity of MinMin to O(KN log N) without affecting its solution quality. Furthermore, we combine the newly proposed MinMin algorithm with MaxMin as well as Sufferage, obtaining two hybrid algorithms. The motivation behind the former hybrid algorithm is to address the drawback of MaxMin in solving problem instances with highly skewed cost distributions while also improving the running time performance of MaxMin. The latter hybrid algorithm improves the running time performance of Sufferage without degrading its solution quality. The proposed algorithms are easy to implement and we illustrate them through detailed pseudocodes. The experimental results over a large number of real-life data sets show that the proposed fast MinMin algorithm and the proposed hybrid algorithms perform significantly better than their traditional counterparts as well as more recent state-of-the-art assignment heuristics. For the large data sets used in the experiments, MinMin, MaxMin, and Sufferage, as well as recent state-of-the-art heuristics, require days, weeks, or even months to produce a solution, whereas all of the proposed algorithms produce solutions within only two or three minutes.

In large-scale commercial web search engines, estimating the importance of a web page is a crucial ingredient in ranking web search results. So far, to assess the importance of web pages, two different types of feedback have been taken into account, independent of each other: the feedback obtained from the hyperlink structure among the web pages (e.g., PageRank) or the web browsing patterns of users (e.g., BrowseRank). Unfortunately, both types of feedback have certain drawbacks. While the former lacks the user preferences and is vulnerable to malicious intent, the latter suffers from sparsity and hence low web coverage. In this work, we combine these two types of feedback under a hybrid page ranking model in order to alleviate the above-mentioned drawbacks. Our empirical results indicate that the proposed model leads to better estimation of page importance according to an evaluation metric that relies on user click feedback obtained from web search query logs. We conduct all of our experiments in a realistic setting, using a very large scale web page collection (around 6.5 billion web pages) and web browsing data (around two billion web page visits).

Data declustering and replication can be used to reduce I/O times related with processing of data intensive queries. Declustering parallelizes the query retrieval process by distributing the data items requested by queries among several disks. Replication enables alternative disk choices for individual disk items and thus provides better query parallelism options. In general, existing replicated declustering schemes do not consider query log information and try to optimize all possible queries for a specific query type, such as range or spatial queries. In such schemes, it is assumed that two or more copies of all data items are to be generated and scheduling of these copies to disks are discussed. However, in some applications, generation of even two copies of all of the data items is not feasible, since data items tend to have very large sizes. In this work, we assume that there is a given limit on disk capacities and thus on replication amounts. We utilize existing query-log information to propose a selective replicated declustering scheme, in which we select the data items to be replicated and decide on their scheduling onto disks while respecting disk capacities. We propose and implement an iterative improvement algorithm to obtain a two-way replicated declustering and use this algorithm in a recursive framework to generate a multiway replicated declustering. Then we improve the obtained multiway replicated declustering by efficient refinement heuristics. Experiments conducted on realistic data sets show that the proposed scheme yields better performance results compared to existing replicated declustering schemes.

In a shared-nothing, distributed text retrieval system, queries are processed over an inverted index that is partitioned among a number of index servers. In practice, the index is either document-based or term-based partitioned. This choice is made depending on the properties of the underlying hardware infrastructure, query traffic distribution, and some performance and availability constraints. In query processing on retrieval systems that adopt a term-based index partitioning strategy, the high communication overhead due to the transfer of large amounts of data from the index servers forms a major performance bottleneck, deteriorating the scalability of the entire distributed retrieval system. In this work, to alleviate this problem, we propose a novel inverted index partitioning model that relies on hypergraph partitioning. In the proposed model, concurrently accessed index entries are assigned to the same index servers, based on the inverted index access patterns extracted from the past query logs. The model aims to minimize the communication overhead that will be incurred by future queries while maintaining the computational load balance among the index servers. We evaluate the performance of the proposed model through extensive experiments using a real-life text collection and a search query sample. Our results show that considerable performance gains can be achieved relative to the term-based index partitioning strategies previously proposed in literature. In most cases, however, the performance remains inferior to that attained by document-based partitioning.

With the advances in cloud computing and huge RAMs provided by 64-bit architectures, it is possible to tackle large problems using memory-based solutions. Construction of term-based, partitioned, parallel inverted indexes is a communication intensive task and suitable for memory-based modeling. In this paper, we provide an efficient parallel framework for in-memory construction of term-based partitioned, inverted indexes. We show that, by utilizing an efficient bucketing scheme, we can eliminate the need for the generation of a global vocabulary. We propose and investigate assignment schemes that can reduce the communication overheads while minimizing the storage and final query processing imbalance. We also present a study on how communication among processors should be carried out with limited communication memory in order to reduce the total inversion time. We present several different communication-memory organizations and discuss their advantages and shortcomings. The conducted experiments indicate promising results.

We study a generalized version of the near-duplicate detection problem which concerns whether a document is a subset of another document. In text-based applications, document containment can be observed in exact-duplicates, near-duplicates, or containments, where the first two are special cases of the third. We introduce a novel method, called CoDet, which focuses particularly on this problem, and compare its performance with four well-known near-duplicate detection methods (DSC, full fingerprinting, I-Match, and SimHash) that are adapted to containment detection. Our method is expandable to different domains, and especially suitable for streaming news. Experimental results show that CoDet effectively and efficiently produces remarkable results in detecting containments.

Concurrently processing thousands of web queries, each with a response time under a fraction of a second, necessitates maintaining and operating massive data centers. For large-scale web search engines, this translates into high energy consumption and a huge electric bill. This work takes the challenge to reduce the electric bill of commercial web search engines operating on data centers that are geographically far apart. Based on the observation that energy prices and query workloads show high spatio-temporal variation, we propose a technique that dynamically shifts the query workload of a search engine between its data centers to reduce the electric bill. Experiments on real-life query workloads obtained from a commercial search engine show that significant financial savings can be achieved by this technique.

The PageRank algorithm is an important component in effective web search. At the core of this algorithm are repeated sparse matrix-vector multiplications where the involved web matrices grow in parallel with the growth of the web and are stored in a distributed manner due to space limitations. Hence, the PageRank computation, which is frequently repeated, must be performed in parallel with high-efficiency and low-preprocessing overhead while considering the initial distributed nature of the web matrices. Our contributions in this work are twofold. We first investigate the application of state-of-the-art sparse matrix partitioning models in order to attain high efficiency in parallel PageRank computations with a particular focus on reducing the preprocessing overhead they introduce. For this purpose, we evaluate two different compression schemes on the web matrix using the site information inherently available in links. Second, we consider the more realistic scenario of starting with an initially distributed data and extend our algorithms to cover the repartitioning of such data for efficient PageRank computation. We report performance results using our parallelization of a state-of-the-art PageRank algorithm on two different PC clusters with 40 and 64 processors. Experiments show that the proposed techniques achieve considerably high speedups while incurring a preprocessing overhead of several iterations (for some instances even less than a single iteration) of the underlying sequential PageRank algorithm.

We introduce a transaction database distribution scheme that divides the frequent item set mining task in a top-down fashion. Our method operates on a graph where vertices correspond to frequent items and edges correspond to frequent item sets of size two. We show that partitioning this graph by a vertex separator is sufficient to decide a distribution of the items such that the subdatabases determined by the item distribution can be mined independently. This distribution entails an amount of data replication, which may be reduced by setting appropriate weights to vertices. The data distribution scheme is used in the design of two new parallel frequent item set mining algorithms. Both algorithms replicate the items that correspond to the separator. NoClique replicates the work induced by the separator and NoClique2 computes the same work collectively. Computational load balancing and minimization of redundant or collective work may be achieved by assigning appropriate load estimates to vertices. The experiments show favorable speedups on a system with small-to-medium number of processors for synthetic and real-world databases.

Query forwarding is an important technique for preserving the result quality in distributed search engines where the index is geographically partitioned over multiple search sites. The key component in query forwarding is the thresholding algorithm by which the forwarding decisions are given. In this paper, we propose a linear-programming-based thresholding algorithm that significantly outperforms the current state-of-the-art in terms of achieved search efficiency values. Moreover, we evaluate a greedy heuristic for partial index replication and investigate the impact of result cache freshness on query forwarding performance. Finally, we present some optimizations that improve the performance further, under certain conditions. We evaluate the proposed techniques by simulations over a real-life setting, using a large query log and a document collection obtained from Yahoo!.

The scheduling of independent but file-sharing tasks on heterogeneous master-slave platforms has recently found important applications in grid environments. The scheduling heuristics recently proposed for this problem are all constructive in nature and based on a common greedy criterion which depends on the momentary completion time values of the tasks. We show that this greedy decision criterion has shortcomings in exploiting the file-sharing interaction among tasks since completion time values are inadequate to extract the global view of this interaction. We propose a three-phase scheduling approach which involves initial task assignment, refinement, and execution ordering phases. For the refinement phase, we model the target application as a hypergraph and, with an elegant hypergraph-partitioning-like formulation, we propose using iterative-improvement-based heuristics for refining the task assignments according to two novel objective functions. Unlike the turnaround time, which is the actual schedule cost, the smoothness of proposed objective functions enables the use of iterative-improvement-based heuristics successfully since their effectiveness and efficiency depend on the smoothness of the objective function. Experimental results on a wide range of synthetically generated heterogeneous master-slave frameworks show that the proposed three-phase scheduling approach performs much better than the greedy constructive approach

We propose a new hypergraph model for the decomposition of irregular computational domains. This work focuses on the decomposition of sparse matrices for parallel matrix-vector multiplication. However, the proposed model can also be used to decompose computational domains of other parallel reduction problems. We propose a “finegrain” hypergraph model for two-dimensional decomposition of sparse matrices. In the proposed fine-grain hypergraph model, vertices represent nonzeros and hyperedges represent sparsity patterns of rows and columns of the matrix. By partitioning the fine-grain hypergraph into equally weighted vertex parts (processors) so that hyperedges are split among as few processors as possible, the model correctly minimizes communication volume while maintaining computationalload balance. Experimental results on a wide range of realistic sparse matrices confirm the validity of the proposed model, by achieving up to 50 percent better decompositionsthan the existing models, in terms of totalcommunication volume. 1

We propose a new two-phase method for the coarse-grain decomposition of irregular computational domains. This work focuses on the 2D partitioning of sparse matrices for parallel matrix-vector multiplication. However, the proposed model can also be used to decompose computational domains of other parallel reduction problems. This work also introduces the use of multi-constraint hypergraph partitioning, for solving the decomposition problem. The proposed method explicitly models the minimization of communication volume while enforcing the upper bound of p + q --- 2 on the maximum number of messages handled by a single processor, for a parallel system with P = p × q processors. Experimental results on a wide range of realistic sparse matrices confirm the validity of the proposed methods, by achieving up to 25 percent better partitions than the standard graph model, in terms of total communication volume, and 59 percent better partitions in terms of number of messages, on the overall average.

In this work, we show that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In the decomposition of the test matrices, the hypergraph models using PaToH and hMeTiS result in up to 63 percent less communication volume (30 to 38 percent less on the average) than the graph model using MeTiS, while PaToH is only 1.3-2.3 times slower than MeTiS on the average.

Optimal load balancing in sparse matrix decomposition without disturbing the row/column ordering is investigated. Both asymptotically and run time efficient exact algorithms are proposed and implemented for one dimensional (1D) striping and two dimensional (2D) jagged partitioning. Binary search method is successfully adopted to 1D striped decomposition by deriving and exploiting a good upper bound on the value of an optimal solution. A binary search algorithm is proposed for 2D jagged partitioning by introducing a new 2D probing scheme. A new iterative refinement scheme is proposed for both 1D and 2D partitioning. The proposed algorithms are also space efficient since they only need the contentional compressed storage scheme for the given matrix, avoiding the need for a dense workload matrix in 2D decomposition. Experimental results on a wide set of test matrices show that considerably better decompositions can be obtained by using optimal load balancing algorithms instead of heuristics. Proposed algorithms are 100 times faster than a single sparse matrix vector multiplication (SpMxV), in the 64 way 1D decompositions, on the overall average. Our jagged partitioning algorithms are only 60% slower than a single SpMxV computation in the 8/spl times/8 way 2D decompositions, on the overall average.

All the previous Kernighan-Lin-based (KL-based) circuit partitioning algorithms employ the locking mechanism, which enforces each cell to move exactly once per pass. In this paper, we propose two novel approaches for multiway circuit partitioning to overcome this limitation. Our approaches allow each cell to move more than once. Our first approach still uses the locking mechanism but in a relaxed way. It introduces the phase concept such that each pass can include more than one phase, and a phase can include at most one move of each cell. Our second approach does not use the locking mechanism at all. It introduces the mobility concept such that each cell can move as freely as allowed by its mobility. Each approach leads to KL-based generic algorithms whose parameters can be set to obtain algorithms with different performance characteristics. We generated three versions of each generic algorithm and evaluated them on a subset of common benchmark circuits in comparison with Sanchis' algorithm (FMS) and the simulated annealing algorithm (SA). Experimental results show that our algorithms are efficient, they outperform FMS significantly, and they perform comparably to SA. Our algorithms perform relatively better as the number of parts in the partition increases as well as the density of the circuit decreases. This paper also provides guidelines for good parameter settings for the generic algorithms.

Although fast Hartley transform (FHT) provides efficient spectral analysis of real discrete signals, the literature that addresses the parallelization of FHT is extremely rare. FHT is a real transformation and does not necessitate any complex arithmetics. On the other hand, FHT algorithm has an irregular computational structure which makes efficient parallelization harder. In this paper, we propose an efficient restructuring for the sequential FHT algorithm which brings regularity and symmetry to the computational structure of the FHT. Then, we propose an efficient parallel FHT algorithm for medium-to-coarse grain hypercube multicomputers by introducing a dynamic mapping scheme for the restructured FHT. The proposed parallel algorithm achieves perfect load-balance, minimizes both the number and volume of concurrent communications, allows only nearest-neighbor communications and achieves in-place computation and communication. The proposed algorithm is implemented on a 32 node iPSC/2 hypercube multicomputer, high-efficiency values are obtained even for small size FHT problems.>

Finite-element discretization produces linear equations in the form Ax=b, where A is large, sparse, and banded with proper ordering of the variables x. The solution of such equations on distributed-memory message-passing multiprocessors implementing the hypercube topology is addressed. Iterative algorithms based on the conjugate gradient method are developed for hypercubes designed for coarse-grained parallelism. The communication requirements of different schemes for mapping finite-element meshes onto the processors of a hypercube are analyzed with respect to the effect of communication parameters of the architecture. Experimental results for a 16-node Intel 80386-based iPSC/2 hypercube are presented and discussed.>