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Register a new userThe Topology of Local Computing in Networks
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Added by
Ami Paz
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed algebraic topology. In both cases, the considered computational model generally assumes communication via shared objects, typically a shared memory consisting of a collection of read-write registers. Our paper is concerned with network computing, where the processes are located at the nodes of a network, and communicate by exchanging messages along the edges of that network. Applying the topological approach for verification in network computing is a considerable challenge, mainly because the presence of identifiers assigned to the nodes yields protocol complexes whose size grows exponentially with the size of the underlying network. However, many of the problems studied in this context are of local nature, and their definitions do not depend on the identifiers or on the size of the network. We leverage this independence in order to meet the above challenge, and present $textit{local}$ protocol complexes, whose sizes do not depend on the size of the network. As an application of the design of compact protocol complexes, we reformulate the celebrated lower bound of $Omega(log^*n)$ rounds for 3-coloring the $n$-node ring, in the algebraic topology framework.
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Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic algorithms. This paper aims at studying randomized synchronous distributed computing through the lens of algebraic topology. We do so by studying the wide class of (input-free) symmetry-breaking tasks, e.g., leader election, in synchronous fault-free anonymous systems. We show that it is possible to redefine solvability of a task locally, i.e., for each simplex of the protocol complex individually, without requiring any global consistency. However, this approach has a drawback: it eliminates the topological aspect of the computation, since a single facet has a trivial topological structure. To overcome this issue, we introduce a projection $pi$ of both protocol and output complexes, where every simplex $sigma$ is mapped to a complex $pi(sigma)$; the later has a rich structure that replaces the structure we lost by considering one single facet at a time. To show the significance and applicability of our topological approach, we derive necessary and sufficient conditions for solving leader election in synchronous fault-free anonymous shared-memory and message-passing models. In both models, we consider scenarios in which there might be correlations between the random values provided to the nodes. In particular, different parties might have access to the same randomness source so their randomness is not independent but equal. Interestingly, we find that solvability of leader election relates to the number of parties that possess correlated randomness, either directly or via their greatest common divisor, depending on the specific communication model.
The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in lock steps, and are failure-free. We show that relaxing these hypotheses to some extent does not hurt local computing. In particular, we show that, for any construction task $T$ associated to a locally checkable labeling (LCL), if $T$ is solvable in $t$ rounds in the LOCAL model, then $T$ remains solvable in $O(t)$ rounds in the asynchronous LOCAL model. This improves the result by Casta~neda et al. [SSS 2016], which was restricted to 3-coloring the rings. More generally, the main contribution of this paper is to show that, perhaps surprisingly, asynchrony and failures in the computations do not restrict the power of the LOCAL model, as long as the communications remain synchronous and failure-free.
In scientific computing, more computational power generally implies faster and possibly more detailed results. The goal of this study was to develop a framework to submit computational jobs to powerful workstations underused by nonintensive tasks. This is achieved by using a virtual machine in each of these workstations, where the computations are done. This group of virtual machines is called the Gridlan. The Gridlan framework is intermediate between the cluster and grid computing paradigms. The Gridlan is able to profit from existing cluster software tools, such as resource managers like Torque, so a user with previous experience in cluster operation can dispatch jobs seamlessly. A benchmark test of the Gridlan implementation shows the systems suitability for computational tasks, principally in embarrassingly parallel computations.
Edge computing offers an additional layer of compute infrastructure closer to the data source before raw data from privacy-sensitive and performance-critical applications is transferred to a cloud data center. Deep Neural Networks (DNNs) are one class of applications that are reported to benefit from collaboratively computing between the edge and the cloud. A DNN is partitioned such that specific layers of the DNN are deployed onto the edge and the cloud to meet performance and privacy objectives. However, there is limited understanding of: (a) whether and how evolving operational conditions (increased CPU and memory utilization at the edge or reduced data transfer rates between the edge and the cloud) affect the performance of already deployed DNNs, and (b) whether a new partition configuration is required to maximize performance. A DNN that adapts to changing operational conditions is referred to as an adaptive DNN. This paper investigates whether there is a case for adaptive DNNs in edge computing by considering three questions: (i) Are DNNs sensitive to operational conditions? (ii) How sensitive are DNNs to operational conditions? (iii) Do individual or a combination of operational conditions equally affect DNNs? (iv) Is DNN partitioning sensitive to hardware architectures on the cloud/edge? The exploration is carried out in the context of 8 pre-trained DNN models and the results presented are from analyzing nearly 8 million data points. The results highlight that network conditions affects DNN performance more than CPU or memory related operational conditions. Repartitioning is noted to provide a performance gain in a number of cases, but a specific trend was not noted in relation to its correlation to the underlying hardware architecture. Nonetheless, the need for adaptive DNNs is confirmed.
In modern distributed computing systems, unpredictable and unreliable infrastructures result in high variability of computing resources. Meanwhile, there is significantly increasing demand for timely and event-driven services with deadline constraints. Motivated by measurements over Amazon EC2 clusters, we consider a two-state Markov model for variability of computing speed in cloud networks. In this model, each worker can be either in a good state or a bad state in terms of the computation speed, and the transition between these states is modeled as a Markov chain which is unknown to the scheduler. We then consider a Coded Computing framework, in which the data is possibly encoded and stored at the worker nodes in order to provide robustness against nodes that may be in a bad state. With timely computation requests submitted to the system with computation deadlines, our goal is to design the optimal computation-load allocation scheme and the optimal data encoding scheme that maximize the timely computation throughput (i.e, the average number of computation tasks that are accomplished before their deadline). Our main result is the development of a dynamic computation strategy called Lagrange Estimate-and Allocate (LEA) strategy, which achieves the optimal timely computation throughput. It is shown that compared to the static allocation strategy, LEA increases the timely computation throughput by 1.4X - 17.5X in various scenarios via simulations and by 1.27X - 6.5X in experiments over Amazon EC2 clusters
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