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parallel Approximate Undirected Shortest Paths via Low Hop Emulators 2020

Parallel Approximate Undirected Shortest Paths via Low Hop E...

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52nd annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Andoni, Alexandr Stein, Clifford Zhong, Peilin Columbia Univ New York NY 10027 USA

ISBN: (纸本)9781450369794

We present a (1 + epsilon) -approximate parallel algorithm for computing shortest paths in undirected graphs, achieving poly(log n) depth and mpoly(log n) work for n-nodes m-edges graphs. Although sequential algorithms with (nearly) optimal running time have been known for several decades, near-optimal parallel algorithms have turned out to be a much tougher challenge. For (1 + epsilon) -approximation, all prior algorithms with poly(log n) depth perform at least Omega(mn(c)) work for some constant c > 0. Improving this long-standing upper bound obtained by Cohen (STOC'94) has been open for 25 years. We develop several new tools of independent interest. One of them is a new notion beyond hopsets - low hop emulator - a poly(log n)-approximate emulator graph in which every shortest path has at most O(log log n) hops (edges). Direct applications of the low hop emulators are parallel algorithms for poly(log n)-approximate single source shortest path (SSSP), Bourgain's embedding, metric tree embedding, and low diameter decomposition, all with poly(log n) depth and mpoly(log n) work. To boost the approximation ratio to (1 + epsilon), we introduce compressible preconditioners and apply it inside Sherman's framework (SODA'17) to solve the more general problem of uncapacitated minimum cost flow (a.k.a., transshipment problem). Our algorithm computes a (1 + epsilon)-approximate uncapacitated minimum cost flow in poly(log n) depth using mpoly(log n) work. As a consequence, it also improves the state-of-the-art sequential running time from m . 2(O(root log n)) to mpoly(log n).

关键词： parallel algorithms shortest paths minimum cost flow low hop emulators

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Unconditional Lower Bounds for Adaptive Massively parallel Computation 20

Unconditional Lower Bounds for Adaptive Massively Parallel C...

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Charikar, Moses Ma, Weiyun Tan, Li-Yang Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9781450369350

We consider unconditional lower bounds in the Adaptive Massively parallel Computation (AMPC) model introduced by Behnezhad et al. (SPAA 19), which is an adaptive variant of the Massively parallel Computation (MPC) model. Our first contribution is an optimal lower bound on the round complexity of distinguishing whether an input graph is a cycle of length n or two cycles of length n/2. This problem, 1v2-Cycle, has emerged as a central problem in the study of modern massively parallel computation. We prove that any AMPC algorithm for the 1v2-Cycle problem with I/O capacity O(n(epsilon)) per machine requires Omega(1/epsilon) rounds, matching the upper bound of Behnezhad et al. More generally, we develop an abstract framework for proving lower bounds in the AMPC model using techniques from Boolean function complexity. Our framework extends the polynomial method of Roughgarden et al. (Jacm 18) for the MPC model in two dimensions: Adaptivity, where machines can write to and adaptively read from shared memory throughout the execution of the computation. Promise problems, where the algorithm only has to succeed on certain inputs. These inputs may have special structure that is of particular interest, or they may be representative of hard instances of the overall problem.

关键词： massively parallel computation adaptive massively parallel computation round complexity lower bounds one cycle vs. two cycles problem

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On the Hardness of Massively parallel Computation 20

On the Hardness of Massively Parallel Computation

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Chung, Kai-Min Ho, Kuan-Yi Sun, Xiaorui Acad Sinica Taipei Taiwan Univ Texas Austin Austin TX 78712 USA Univ Illinois Chicago IL 60680 USA

ISBN: (纸本)9781450369350

We investigate whether there are inherent limits of parallelization in the (randomized) massively parallel computation (MPC) model by comparing it with the (sequential) RAM model. As our main result, we show the existence of hard functions that are essentially not parallelizable in the MPC model. Based on the widely-used random oracle methodology in cryptography with a cryptographic hash function h : {0, 1}(n) -> {0, 1}(n) computable in time t(h), we show that there exists a function that can be computed in time O(T center dot t(h)) and space S by a RAM algorithm, but any MPC algorithm with local memory size s < S/c for some c > 1 requires at least (Omega) over tilde (T)(1) rounds to compute the function, even in the average case, for a wide range of parameters n <= S <= T <= 2(n1/4). Our result is almost optimal in the sense that by taking T to be much larger than t(h), e.g., T to be sub-exponential in t(h), to compute the function, the round complexity of any MPC algorithm with small local memory size is asymptotically the same (up to a polylogarithmic factor) as the time complexity of the RAM algorithm. Our result is obtained by adapting the so-called compression argument from the data structure lower bounds and cryptography literature to the context of massively parallel computation.

关键词： lower bound of communication rounds massively parallel computation random oracle model

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An Overview of Reference architectures for Cloud of Things 20

An Overview of Reference Architectures for Cloud of Things

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35th annual acm symposium on Applied Computing (SAC)

作者： Dias, Diogenes Delicato, Flavia C. Pires, Paulo F. Rocha, Atslands R. Nakagawa, Elisa Y. Univ Sao Paulo Sao Carlos Brazil Fluminense Fed Univ Niteroi RJ Brazil Fed Univ Ceara UFC Fortaleza Ceara Brazil

ISBN: (纸本)9781450368667

Cloud of Things (CoT) is a new paradigm that explores the synergy between Internet of Things (IoT) and cloud computing and has increasingly promoted the development of complex software intensive systems in diverse and even critical application domains. In parallel, reference architectures have contributed as a means to capture the knowledge of how to develop, standardize, and evolve software-intensive systems and, as a consequence, have promoted quality issues in different domains. However, there is still a lack of investigation on reference architectures for CoT, which could be impacting the lack of standardization in CoT systems. Hence, the main contribution of this paper is to present an overview of reference architectures for CoT and, for this, we conducted a systematic mapping study (SMS) and found eight architectures proposed quite recently in different application domains. As a result, these architectures have advanced mainly in terms of standardization, but they have not still large dissemination and wider adoption by the software industry. Several open issues can be pointed out, including actions to promote the sustainability of these architectures.

关键词： Internet of Things Cloud Computing Cloud of Things Reference Architecture Systematic Mapping Study

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parallel Machine Scheduling to Minimize Energy Consumption 31

Parallel Machine Scheduling to Minimize Energy Consumption

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31st annual acm-SIAM symposium on Discrete algorithms (SODA)

作者： Antoniadis, Antonios Garg, Naveen Kumar, Gunjan Kumar, Nikhil Saarland Univ Saarland Univ Campus Saarbrucken Germany Max Planck Inst Informat Saarland Univ Campus Saarbrucken Germany Indian Inst Technol Delhi New Delhi India Tata Inst Fundamental Res Mumbai Maharashtra India

ISBN: (纸本)9781611975994

Given n jobs with release dates, deadlines and processing times we consider the problem of scheduling them on m parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in this state. Each machine requires L units of energy to awaken from the sleep state and in its active state the machine can process jobs and consumes a unit of energy per unit time. We allow for preemption and migration of jobs and provide the first constant approximation algorithm for this problem.

关键词： Energy utilization

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Randomized Incremental Convex Hull is Highly parallel 20

Randomized Incremental Convex Hull is Highly Parallel

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Blelloch, Guy E. Gu, Yan Shun, Julian Sun, Yihan Carnegie Mellon Univ Pittsburgh PA 15213 USA UC Riverside Riverside CA USA MIT CSAIL 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781450369350

The randomized incremental convex hull algorithm is one of the most practical and important geometric algorithms in the literature. Due to its simplicity, and the fact that many points or facets can be added independently, it is also widely used in parallel convex hull implementations. However, to date there have been no non-trivial theoretical bounds on the parallelism available in these implementations. In this paper, we provide a strong theoretical analysis showing that the standard incremental algorithm is inherently parallel. In particular, we show that for n points in any constant dimension, the algorithm has O(logn) dependence depth with high probability. This leads to a simple work-optimal parallel algorithm with polylogarithmic span with high probability. Our key technical contribution is a new definition and analysis of the configuration dependence graph extending the traditional configuration space, which allows for asynchrony in adding configurations. To capture the "true" dependence between configurations, we define the support set of configuration c to be the set of already added configurations that it depends on. We show that for problems where the size of the support set can be bounded by a constant, the depth of the configuration dependence graph is shallow ( O(logn) with high probability for input size n). In addition to convex hull, our approach also extends to several related problems, including half-space intersection and finding the intersection of a set of unit circles. We believe that the configuration dependence graph and its analysis is a general idea that could potentially be applied to more problems.

关键词： convex hull configuration space parallelism randomized incremental algorithms

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parallel Load Balancing on Constrained Client-Server Topologies 20

Parallel Load Balancing on Constrained Client-Server Topolog...

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Clementi, Andrea Natale, Emanuele Ziccardi, Isabella Univ Roma Tor Vergata Rome Italy Univ Cote Azur INRIA CNRS Sophia Antipolis France Univ Aquila Laquila Italy

ISBN: (纸本)9781450369350

We study parallel Load Balancing protocols for a client-server distributed model defined as follows. There is a set C of n clients and a set S of n servers where each client has (at most) a constant number d >= 1 of requests that must be assigned to some server. The client set and the server one are connected to each other via a fixed bipartite graph: the requests of client v can only be sent to the servers in its neighborhood N(v). The goal is to assign every client request so as to minimize the maximum load of the servers. In this setting, efficient parallel protocols are available only for dense topolgies. In particular, a simple symmetric, non-adaptive protocol achieving constant maximum load has been recently introduced by Becchetti et al [4] for regular dense bipartite graphs. The parallel completion time is O(logn) and the overall work is O(n), w.h.p. Motivated by proximity constraints arising in some client-server systems, we devise a simple variant of Becchetti et al's protocol [4] and we analyse it over almost-regular bipartite graphs where nodes may have neighborhoods of small size. In detail, we prove that, w.h.p., this new version has a cost equivalent to that of Becchetti et al's protocol (in terms of maximum load, completion time, and work complexity, respectively) on every almost-regular bipartite graph with degree Omega(log(2) n). Our analysis significantly departs from that in [4] for the original protocol and requires to cope with non-trivial stochastic-dependence issues on the random choices of the algorithmic process which are due to the worst-case, sparse topology of the underlying graph.

关键词： parallel Balanced Allocations Balls-into-Bins Processes Randomized algorithms

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Green Paging and parallel Paging 20

Green Paging and Parallel Paging

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32nd acm symposium on parallelism in algorithms and architectures, SPAA 2020

作者： Agrawal, Kunal Bender, Michael A. Das, Rathish Kuszmaul, William Peserico, Enoch Scquizzato, Michele Washington University in St. Louis St. LouisMO United States Stony Brook University Stony BrookNY United States Massachusetts Institute of Technology CambridgeMA United States University of Padova Padova Italy

ISBN: (纸本)9781450369350

We study two fundamental variants of the classic paging problem: green paging and parallel paging. In green paging one can choose the exact memory capacity in use at any given instant, between a maximum of k and a minimum of k/p pages;the goal is to minimize the integral of this number over the time required to complete a computation (note that running at lower capacity is not necessarily better, since might disproportionately increase the total completion time). In parallel paging, a memory of k pages is shared between p processors, each carrying out a separate computation;the goal is to minimize the respective completion times. We show how these two different problems are strictly related: any efficient solution to green paging can be converted into an efficient solution to parallel paging, and any lower bound for green paging can be converted into a lower bound for parallel paging - -in both cases in a black-box fashion. Exploiting this relation, we provide tight upper and lower bounds of (log p) on the competitive ratio with O(1) resource augmentation for both problems. © 2020 Owner/Author.

关键词： Green computing

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Efficient, Distributed, and Non-Speculative Multi-Address Atomic Operations 21

Efficient, Distributed, and Non-Speculative Multi-Address At...

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54th annual IEEE/acm International symposium on Microarchitecture (MICRO)

作者： Jose Gomez-Hernandez, Eduardo Cebrian, Juan M. Titos-Gil, Ruben Kaxiras, Stefanos Ros, Alberto Univ Murcia Dept Comp Engn Murcia Spain Uppsala Univ Dept Informat Technol Uppsala Sweden

ISBN: (纸本)9781450385572

Critical sections that read, modify, and write (RMW) a small set of addresses are common in parallel applications and concurrent data structures. However, to escape from the intricacies of finegrained locks, which require reasoning about all possible thread interleavings, programmers often resort to coarse-grained locks to ensure atomicity. This results in atomic protection of a much larger set of potentially conflicting addresses, and, consequently, increased lock contention and unneeded serialization. As many before us have observed, these problems would be solved if only general RMW multi-address atomic operations were available, but current proposals are impractical because of deadlock scenarios that appear due to resource limitations. Alternatively, transactional memory can detect conflicts at run-time aiming to maximize concurrency, but it has significant overheads in highly-contended critical sections. In this work, we propose multi-address atomic operations (MAD atomics). MADatomics achieve complexity-effective, non-speculative, non-deadlocking, fine-grained locking for multiple addresses, relying solely on the coherence protocol and a predetermined locking order. Unlike prior works, MAD atomics address the challenge of enabling atomic modification over a set of cachelines with arbitrary addresses, simultaneously locking all of them while sidestepping deadlock. MAD atomics only require a small storage per core (around 68 bytes), while significantly outperforming typical lock implementations. Indeed, our evaluation using gem5-20 shows that MAD atomics can improve performance by up to 18x (3.4x, on average, for the applications and concurrent data structures evaluated in this work) over a baseline implemented with locks running on 16 cores. More importantly, the improvement still reaches 2.7x, on average, compared to an Intel hardware transactional memory implementation running on 16 cores.

关键词： Multi-core architectures synchronization critical sections atomicity multi-address atomics

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Graph Sparsification for Derandomizing Massively parallel Computation with Low Space 20

Graph Sparsification for Derandomizing Massively Parallel Co...

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Czumaj, Artur Davies, Peter Parter, Merav Univ Warwick Coventry W Midlands England IST Austria Klosterneuburg Austria Weizmann Inst Sci Rehovot Israel

ISBN: (纸本)9781450369350

Massively parallel Computation (MPC) is an emerging model which distills core aspects of distributed and parallel computation. It was developed as a tool to solve (typically graph) problems in systems where input is distributed over many machines with limited space. Recent work has focused on the regime in which machines have sublinear (in. n, number of nodes in the input graph) space, with randomized algorithms presented for the fundamental problems of Maximal Matching and Maximal Independent Set. There are, however, no prior corresponding deterministic algorithms. A major challenge in the sublinear space setting is that the local space of each machine may be too small to store all the edges incident to a single node. To overcome this barrier we introduce a new graph sparsification technique that deterministically computes a low-degree subgraph with additional desired properties: degrees in the subgraph are sufficiently small that nodes' neighborhoods can be stored on single machines, and solving the problem on the subgraph provides significant global progress towards solving the problem for the original input graph. Using this framework to derandomize the well-known randomized algorithm of Luby [SICOMP'86], we obtain O(log Delta + log log n)-round deterministic MPC algorithms for solving the fundamental problems of Maximal Matching and Maximal Independent Set with O(n(epsilon)) space on each machine for any constant epsilon > 0. Based on the recent work of Ghaffari et al. [FOCS'18], this additive O(log log n) factor is conditionally essential. These algorithms can also be shown to run in O(log Delta) rounds in the closely related model of CONGESTED CLIQUE, improving upon the state-of-the-art bound of O(log(2) Delta) rounds by Censor-Hillel et al. [DISC'17].

关键词： Massively parallel Computation Derandomization Maximal Independent Set Maximal Matching Low Space

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