Abstract

We study several fundamental problems in the kmachine model, a message-passing model for large-scale distributed computations where k 2 machines jointly perform computations on a large input of size N, (typically, N k). The input is initially partitioned (randomly or in a balanced fashion) among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main result is a general technique for designing efficient deterministic distributed algorithms in the k-machine model using PRAM algorithms. Our technique works by efficiently simulating PRAM algorithms in the k-machine model in a deterministic way. This simulation allows us to arrive at new algorithms in the k-machine model for some problems for which no efficient k-machine algorithms are known before and also improve on existing results in the k-machine model for some problems. While our simulation allows us to obtain k-machine algorithms for any problem with a known PRAM algorithm, we mainly focus on graph problems. For an input graph on n vertices and m edges, we obtain O˜(m/k2) round4 algorithms for various graph problems such as r–connectivity for r = 1, 2, 3, 4, minimum spanning tree (MST), maximal independent set (MIS), (Δ+1)-coloring, maximal matching, ear decomposition, and spanners under the assumption that the edges of the input graph are partitioned (randomly, or in an arbitrary, but balanced, fashion) among the k machines. For problems such as connectivity and MST, the above bound is (essentially) the best possible (up to logarithmic factors). Our simulation technique allows us to obtain the first known efficient deterministic algorithms in the k-machine model for other problems with known deterministic PRAM algorithms.

Abstract

Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al.~PODC 2019; Ghaffari-Uitto SODA 2019), we investigate the complexity of ruling set problems in this model. The MPC model has become very popular as a model for large-scale distributed computing and it comes with the constraint that the memory-per-machine is strongly sublinear in the input size. For graph problems, extremely fast MPC algorithms have been designed assuming Ω~(n) memory-per-machine, where n is the number of nodes in the graph (e.g., the O(loglogn) MIS algorithm of Ghaffari et al., PODC 2018). However, it has proven much more difficult to design fast MPC algorithms for graph problems in the low-memory MPC model, where the memory-per-machine is restricted to being strongly sublinear in the number of nodes, i.e., $O(n^eps)$ for $0 < eps < 1$. In this paper, we present an algorithm for the 2-ruling set problem, running in O~(log1/6Δ) rounds whp, in the low-memory MPC model. We then extend this result to β-ruling sets for any integer β>1. Specifically, we show that a β-ruling set can be computed in the low-memory MPC model with $O(n^eps)$ memory-per-machine in O~(β⋅log1/(2β+1−2)Δ) rounds, whp. From this it immediately follows that a β-ruling set for β=Ω(logloglogΔ)-ruling set can be computed in in just O(βloglogn) rounds whp. The above results assume a total memory of $tilde{O}(m + n^{1+eps})$. We also present algorithms for β-ruling sets in the low-memory MPC model assuming that the total memory over all machines is restricted to O~(m).

Abstract

Finding the centrality measures of nodes in a graph is a problem of fundamental importance due to various applications from social networks, biological networks, and transportation networks. Given the large size of such graphs, it is natural to use parallelism as a recourse. There have been several studies that show how to compute the various centrality measures of nodes in a graph on parallel architectures, including multi-core systems and GPUs. However, as these graphs evolve and change, it is pertinent to study how to update the centrality measures on changes to the underlying graph. In this paper, we show novel parallel algorithms for updating the betweenness- and closeness-centrality values of nodes in a dynamic graph. Our algorithms process a batch of updates in parallel by extending the approach of handling a single update for etweennessand closeness-centrality by Jamour et al. [16] and Sarıyüce et al. [27], respectively. Besides, our algorithms incorporate mechanisms to exploit the structural properties of graphs for enhanced performance.

Abstract

In this paper, we study scalable parallel algorithms for estimating the farness-centrality value of the nodes in a given undirected and connected graph. Our algorithms consider approaches that are more suitable for sparse graphs. To this end, we propose four optimization techniques based on removing redundant nodes, removing identical nodes, removing chain nodes, and making use of decomposition based on the biconnected components of the input graph. We test our techniques on a collection of real-world graphs for the time taken and the average error percentage. We further analyze the applicability of our techniques on various classes of real-world graphs. We suggest why certain techniques work better on certain classes of graphs.

Abstract

A large portion of the computation in sparse neural networks comprises of multiplying a sparse matrix with a dense matrix, denoted SDMM in this paper. The SDMM operation with an unstructured sparsity pattern cannot be efficiently processed on modern architectures such as GPUs due to irregularity in compute and memory accesses. However, efficient parallel algorithms on a GPU can be designed for SDMM when the sparsity pattern is more structured. Thus, the run time performance of sparse neural networks on a GPU is dependent on the sparsity pattern present in the underlying matrix.In sparse neural networks obtained using pruning based approaches, the choice of sparsity pattern not only effects the run time, but also effects the accuracy of the task for which the neural network is trained for. Sparsity patterns which have a good run time performance on a GPU may not have a good accuracy and vice-versa. The real challenge then is to given a target architecture, identify a sparsity pattern, a storage format,and an algorithm for SDMM that leads to sparse neural networks which are efficient in both run time and accuracy.In this work, we propose a novel, structured, flexible, and generic sparsity pattern called the RMB (Regularized MultiBlock) sparsity pattern, and an efficient storage format (CRMB),and a fast GPU algorithm for processing RMBMM (SDMMwith the multiplicand having RMB sparsity pattern). Using theRMB sparsity pattern, we achieve better trade-offs between the accuracy, and the run time performance of sparse neural networks on a GPU when compared to commonly used sparsity patterns like unstructured, and block sparsity patterns.

Abstract

In this paper, we study scalable parallel algorithms for estimating the farness-centrality value of the nodes in a given undirected and connected graph. Our algorithms consider approaches that are more suitable for sparse graphs. To this end, we propose four optimization techniques based on removing redundant nodes, removing identical nodes, removing chain nodes, and making use of decomposition based on the biconnected components of the input graph.We test our techniques on a collection of real-world graphs for the time taken and the average error percentage. We further analyze the applicability of our techniques on various classes of real-world graphs. We suggest why certain techniques work better on certain classes of graphs

Abstract

We focus on the problem of symmetric key distribution for securing shared resources among large groups of users in distributed applications like cloud storage, shared databases, and collaborative editing, among others. In such applications, resources such as data, are sensitive in nature and it is necessary that only authorized users are allowed access without the presence of on-line monitoring system. The de-facto approach is to encrypt a shared resource and deploy a key distribution mechanism, which enables only authorized users to generate the respective decryption key for the resource. The key distribution approach has two major challenges: first, the applications are dynamic i.e., users might join and leave arbitrarily, and second, for a large number of users, it is required that the cryptographic technique be scalable and efficient. In this work, we describe an approach that overcomes these challenges by using two key techniques: first, flattening the access structure and applying efficient symmetric key distribution techniques. By flattening the access structure, we reduce the problem to that of key distribution of a resource among all the users sharing that resource. We consider this smaller flattened access structure and devise a unified key distribution technique that is sufficient for key distribution across all such structures. Our key distribution techniques have an important feature of a public secret and a private secret, which allows the group controller to publish updates to the keying material using the public secret and therefore, does not necessitate the users to be in constant communication with the group controller. Using this model we describe two efficient key distribution techniques that scale logarithmically with the group size and also handle group additions and removals. Furthermore, a user can be off-line for any amount of time and need not be aware of the dynamics of the system, which is important as it overcomes the problems posed by lossy channels. We have performed an experimental evaluation of our scheme against a popular existing scheme and show that they perform better for this scheme with the same security guarantees. As our approaches are easy to implement they are especially suitable for practical applications where security is viewed as an overhead rather than as a necessity.

Abstract

Sparse neural networks are efficient in both memory and compute when compared to dense neural networks. But on parallel hardware such as GPU, sparse neural networks result in small or no runtime performance gains. On the other hand, structured sparsity patterns like filter, channel and block sparsity result in large performance gains due to regularity induced by structure. Among structured sparsities, block sparsity is a generic structured sparsity pattern with filter and channel sparsity being sub cases of block sparsity. In this work, we focus on block sparsity and generate efficient block sparse convolutional neural networks using our approach DBSR (Dynamic block sparse reparameterization). Our DBSR approach, when applied on image classification task over Imagenet dataset, decreases parameters and FLOPS of ResneXt50 by a factor of 2x with only increase of 0.48 in Top-1 error. And when extended to the task of semantic segmentation, our approach reduces parameters and FLOPS by 30% and 20% respectively with only 1% decrease in mIoU for ERFNet over Cityscapes dataset

Abstract

Finding whether a graph is k-connected, and the identification of its k-connected components is a fundamental problem in graph theory. For this reason, there have been several algorithms for this problem in both the sequential and parallel settings. Several recent sequential and parallel algorithms fork-connectivity rely on one or more breadth-first traversals of the input graph.While BFS can be made very efficient in a sequential setting,the same cannot be said in the case of parallel environments. A major factor in this difficulty is due to the inherent requirement to use a shared queue, balance work among multiple threads in every round, synchronization, and the like. Optimizing the execution of BFS on many current parallel architectures is therefore quite challenging. For this reason, it can be noticed that the time spent by the current parallel graph connectivity algorithms on BFS operations is usually a significant portion of their overall runtime.In this paper, we study how one can, in the context of algorithms for graph connectivity, mitigate the practical in efficiency of relying on BFS operations in parallel. Our technique suggests that such algorithms may not require a BFS of the input graph but actually can work with a sparse spanning subgraph of the input graph. The incorrectness introduced by not using a BFS spanning tree can then be offset by further post-processing stepson suitably defined small auxiliary graphs. Our experiments on finding the 2, and 3-connectivity of graphs on Nvidia K40c GPUs improve the state-of-the-art on the corresponding problems by a factor 2.2x, and 2.1x respectively

Abstract

Graph algorithms play an important role in several fields of sciences and engineering. Prominent among them are the All-Pairs-Shortest-Paths (APSP) and related problems. Indeed there are several efficient implementations for such problems on a variety of modern multi- and manycore architectures. It can be noticed that for several graph problems, parallelism offers only a limited success as current parallel architectures have severe short-comings when deployed for most graph algorithms. At the same time, some of these graphs exhibit clear structural properties due to their sparsity. This calls for particular solution strategies aimed at scalable processing of large, sparse graphs on modern parallel architectures. In this paper, we study the applicability of an ear decomposition of graphs to problems such as all-pairs-shortest-paths and minimum cost cycle basis. Through experimentation, we show that the resulting solutions are scalable in terms of both memory usage and also their speedup over best known current implementations. We believe that our techniques have the potential to be relevant for designing scalable solutions for other computations on large sparse graphs.