Due to mainstream adoption of cloud computing and its rapidly increasing usage of energy, the efficient management of cloud computing resources has become an important issue. A key challenge in managing the resources lies in the volatility of their demand. While there have been a wide variety of online algorithms (e.g. Receding Horizon Control, Online Balanced Descent) designed, it is hard for cloud operators to pick the right algorithm. In particular, these algorithms vary greatly on their usage of predictions and performance guarantees. This paper aims at studying an automatic algorithm selection scheme in real time. To do this, we empirically study the prediction errors from real-world cloud computing traces. Results show that prediction errors are distinct from different prediction algorithms, across virtual machines, and over the time horizon. Based on these observations, we propose a simple prediction error model and prove upper bounds on the dynamic regret of several online algorithms. We then apply the empirical and theoretical results to create a simple online meta-algorithm that chooses the best algorithm on the fly. Numerical simulations demonstrate that the performance of the designed policy is close to that of the best algorithm in hindsight.
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Precise Error Estimation for Sketch-based Flow Measurement
As a class of approximate measurement approaches, sketching algorithms have significantly improved the estimation of network flow information using limited resources. While these algorithms enjoy sound error-bound analysis under worst-case scenarios, their actual errors can vary significantly with the incoming flow distribution, making their traditional error bounds too "loose" to be useful in practice. In this paper, we propose a simple yet rigorous error estimation method to more precisely analyze the errors for posterior sketch queries by leveraging the knowledge from the sketch counters. This approach will enable network operators to understand how accurate the current measurements are and make appropriate decisions accordingly (e.g., identify potential heavy users or answer "what-if" questions to better provision resources). Theoretical analysis and trace-driven experiments show that our estimated bounds on sketch errors are much tighter than previous ones and match the actual error bounds in most cases.
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- PAR ID:
- 10343435
- Date Published:
- Journal Name:
- Proceedings of the 21st ACM Internet Measurement Conference (IMC '21)
- Page Range / eLocation ID:
- 113 to 121
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Per-flow size measurement is key to many streaming applications and management systems, particularly in high-speed networks. Performing such measurement on the data plane of a network device at the line rate requires on-chip memory and computing resources that are shared by other key network functions. It leads to the need for very compact and fast data structures, called sketches, which trade off space for accuracy. Such a need also arises in other application context for extremely large data sets. The goal of sketch design is two-fold: to measure flow size as accurately as possible and to do so as efficiently as possible (for low overhead and thus high processing throughput). The existing sketches can be broadly categorized to multi-update sketches and single update sketches. The former are more accurate but carry larger overhead. The latter incur small overhead but their accuracy is poor. This paper proposes a Single update Sketch with a Variable counter Structure (SSVS), a new sketch design which is several times faster than the existing multi-update sketches with comparable accuracy, and is several times more accurate than the existing single update sketches with comparable overhead. The new sketch design embodies several technical contributions that integrate the enabling properties from both multi-update sketches and single update sketches in a novel structure that effectively controls the measurement error with minimum processing overhead.
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Estimating the ε-approximate quantiles or ranks of a stream is a fundamental task in data monitoring. Given a stream x_1,..., x_n from a universe \mathcalU with total order, an additive-error quantile sketch \mathcalM allows us to approximate the rank of any query y\in \mathcalU up to additive ε n error. In 2001, Greenwald and Khanna gave a deterministic algorithm (GK sketch) that solves the ε-approximate quantiles estimation problem using O(ε^-1 łog(ε n)) space \citegreenwald2001space ; recently, this algorithm was shown to be optimal by Cormode and Vesleý in 2020 \citecormode2020tight. However, due to the intricacy of the GK sketch and its analysis, over-simplified versions of the algorithm are implemented in practical applications, often without any known theoretical guarantees. In fact, it has remained an open question whether the GK sketch can be simplified while maintaining the optimal space bound. In this paper, we resolve this open question by giving a simplified deterministic algorithm that stores at most (2 + o(1))ε^-1 łog (ε n) elements and solves the additive-error quantile estimation problem; as a side benefit, our algorithm achieves a smaller constant factor than the \frac11 2 ε^-1 łog(ε n) space bound in the original GK sketch~\citegreenwald2001space. Our algorithm features an easier analysis and still achieves the same optimal asymptotic space complexity as the original GK sketch. Lastly, our simplification enables an efficient data structure implementation, with a worst-case runtime of O(łog(1/ε) + łog łog (ε n)) per-element for the ordinary ε-approximate quantile estimation problem. Also, for the related weighted'' quantile estimation problem, we give efficient data structures for our simplified algorithm which guarantee a worst-case per-element runtime of O(łog(1/ε) + łog łog (ε W_n/w_\textrmmin )), achieving an improvement over the previous upper bound of \citeassadi2023generalizing.
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null (Ed.)Abstract In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first investigate necessary and sufficient conditions for the sketch sampling to have well-defined algorithms. Based on these sampling conditions we develop new sketch descent methods for solving general smooth linearly constrained problems, in particular, random sketch descent (RSD) and accelerated random sketch descent (A-RSD) methods. To our knowledge, this is the first convergence analysis of RSD algorithms for optimization problems with multiple non-separable linear constraints. For the general case, when the objective function is smooth and non-convex, we prove for the non-accelerated variant sublinear rate in expectation for an appropriate optimality measure. In the smooth convex case, we derive for both algorithms, non-accelerated and A-RSD, sublinear convergence rates in the expected values of the objective function. Additionally, if the objective function satisfies a strong convexity type condition, both algorithms converge linearly in expectation. In special cases, where complexity bounds are known for some particular sketching algorithms, such as coordinate descent methods for optimization problems with a single linear coupled constraint, our theory recovers the best known bounds. Finally, we present several numerical examples to illustrate the performances of our new algorithms.more » « less
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The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3487552.3487856
