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Mining Circuit Lower Bound Proofs for meta-algorithms

COMPUTATIONAL COMPLEXITY 2015年第2期24卷 333-392页

作者： Chen, Ruiwen Kabanets, Valentine Kolokolova, Antonina Shaltiel, Ronen Zuckerman, David Simon Fraser Univ Sch Comp Sci Burnaby BC V5A 1S6 Canada Mem Univ Newfoundland Dept Comp Sci St John NF A1C 5S7 Canada Univ Haifa Dept Comp Sci IL-31999 Haifa Israel Univ Texas Austin Dept Comp Sci Austin TX 78712 USA

We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for "easy" Boolean functions from the corresponding circuit classes. The compression problem is defined as follows: given the truth table of an n-variate Boolean function f computable by some unknown small circuit from a known class of circuits, find in deterministic time poly(2 (n) ) a circuit C (no restriction on the type of C) computing f so that the size of C is less than the trivial circuit size . We get non-trivial compression for functions computable by AC (0) circuits, (de Morgan) formulas, and (read-once) branching programs of the size for which the lower bounds for the corresponding circuit class are known. These compression algorithms rely on the structural characterizations of "easy" functions, which are useful both for proving circuit lower bounds and for designing "meta-algorithms" (such as Circuit-SAT). For (de Morgan) formulas, such structural characterization is provided by the "shrinkage under random restrictions" results by Subbotovskaya (Doklady Akademii Nauk SSSR 136(3):553-555, 1961) and HAyenstad (SIAM J Comput 27:48-64, 1998), strengthened to the "high-probability" version by Santhanam (Proceedings of the Fifty-First Annual IEEE Symposium on Foundations of Computer Science, pp 183-192, 2010), Impagliazzo, Meka & Zuckerman (Proceedings of the Fifty-Third Annual IEEE Symposium on Foundations of Computer Science, pp 111-119, 2012b), and Komargodski & Raz (Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp 171-180, 2013). We give a new, simple proof of the "high-probability" version of the shrinkage result for (de Morgan) formulas, with improved parameters. We use this shrinkage result to get both compression and #SAT algorithms for (de Morgan) formulas of size about n (2). We also use this shrinkage result to get an alternative proof of the result by Komargodski & Raz (Proceedings of the Forty-Fi

关键词： Average-case circuit lower bounds Circuit-SAT algorithms compression meta-algorithms natural property random restrictions shrinkage of de Morgan formulas

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Mining Circuit Lower Bound Proofs for meta-algorithms

Mining Circuit Lower Bound Proofs for Meta-Algorithms

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IEEE 29th Conference on Computational Complexity (CCC)

作者： Chen, Ruiwen Kabanets, Valentine Kolokolova, Antonina Shaltiel, Ronen Zuckerman, David Simon Fraser Univ Sch Comp Sci Burnaby BC V5A 1S6 Canada Mem Univ Newfoundland Dept Comp Sci St John NF Canada Univ Haifa Dept Comp Sci Haifa Israel Univ Texas Austin Dept Comp Sci Austin TX 78712 USA

ISBN: (纸本)9781479936267

We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for "easy" Boolean functions from the corresponding circuit classes. The compression problem is defined as follows: given the truth table of an n-variate Boolean function f computable by some unknown small circuit from a known class of circuits, find in deterministic time poly(2(n)) a circuit C (no restriction on the type of C) computing f so that the size of C is less than the trivial circuit size 2(n)/n. We get non-trivial compression for functions computable by AC(0) circuits, (de Morgan) formulas, and (read-once) branching programs of the size for which the lower bounds for the corresponding circuit class are known. These compression algorithms rely on the structural characterizations of "easy" functions, which are useful both for proving circuit lower bounds and for designing "meta-algorithms" (such as Circuit-SAT). For (de Morgan) formulas, such structural characterization is provided by the "shrinkage under random restrictions" results [52], [21], strengthened to the "high-probability" version by [48], [26], [33]. We give a new, simple proof of the "high-probability" version of the shrinkage result for (de Morgan) formulas, with improved parameters. We use this shrinkage result to get both compression and #SAT algorithms for (de Morgan) formulas of size about n(2). We also use this shrinkage result to get an alternative proof of the recent result by Komargodski and Raz [33] of the average-case lower bound against small (de Morgan) formulas. Finally, we show that the existence of any non-trivial compression algorithm for a circuit class C subset of P/poly would imply the circuit lower bound NEXP not subset of C. This complements Williams's result [55] that any non-trivial Circuit-SAT algorithm for a circuit class C would imply a superpolynomial lower bound against C for a language in NEXP1.

关键词： average-case circuit lower bounds Circuit-SAT algorithms compression meta-algorithms natural property random restrictions shrinkage of de Morgan formulas

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Sparkle: Toward Accessible meta-Algorithmics for Improving the State of the Art in Solving Challenging Problems

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2022年第6期26卷 1351-1364页

作者： Van der Blom, Koen Hoos, Holger H. H. Luo, Chuan Rook, Jeroen G. G. Leiden Univ Fac Sci NL-2311 EZ Leiden Netherlands Sorbonne Univ LIP6 CNRS F-75005 Paris France Rhein Westfal TH Aachen Dept Comp Sci D-52062 Aachen Germany Univ British Columbia Dept Comp Sci Vancouver BC V6T 1Z4 Canada Beihang Univ Sch Software Beijing 100190 Peoples R China Univ Twente Data Management & Biometr DMB NL-7522 NB Enschede Netherlands

Many fields of computational science advance through improvements in the algorithms used for solving key problems. These advancements are often facilitated by benchmarks and competitions that enable performance comparisons and rankings of solvers. Simultaneously, meta-algorithmic techniques, such as automated algorithm selection and configuration, enable performance improvements by utilizing the complementary strengths of different algorithms or configurable algorithm components. In fact, meta-algorithms have become major drivers in advancing the state of the art in solving many prominent computational problems. However, meta-algorithmic techniques are complex and difficult to use correctly, while their incorrect use may reduce their efficiency, or in extreme cases, even lead to performance losses. Here, we introduce the Sparkle platform, which aims to make meta-algorithmic techniques more accessible to nonexpert users, and to make these techniques more broadly available in the context of competitions, to further enable the assessment and advancement of the true state of the art in solving challenging computational problems. To achieve this, Sparkle implements standard protocols for algorithm selection and configuration that support easy and correct use of these techniques. Following an experiment, Sparkle generates a report containing results, problem instances, algorithms, and other relevant information, for convenient use in scientific publications.

关键词： Algorithm configuration algorithm selection benchmarking competitions meta-algorithms software tools

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A PAC APPROACH TO APPLICATION-SPECIFIC ALGORITHM SELECTION

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SIAM JOURNAL ON COMPUTING 2017年第3期46卷 992-1017页

作者： Gupta, Rishi Roughgarden, Tim Stanford Univ Dept Comp Sci Stanford CA 94305 USA

The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large body of literature on empirical approaches to selecting the best algorithm for a given application domain, there has been surprisingly little theoretical analysis of the problem. This paper adapts concepts from statistical and online learning theory to reason about application-specific algorithm selection. Our models capture several state-of-the-art empirical and theoretical approaches to the problem, ranging from self-improving algorithms to empirical performance models, and our results identify conditions under which these approaches are guaranteed to perform well. We present one framework that models algorithm selection as a statistical learning problem, and our work here shows that dimension notions from statistical learning theory, historically used to measure the complexity of classes of binary-and real-valued functions, are relevant in a much broader algorithmic context. We also study the online version of the algorithm selection problem, and give possibility and impossibility results for the existence of no-regret learning algorithms.

关键词： algorithm selection parameter tuning PAC learning online learning meta-algorithms

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Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

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ELECTRONICS LETTERS 2012年第21期48卷 1357-1358页

作者： Shaver, A. Hadjiloucas, S. Walker, G. C. Bowen, J. W. Univ Reading Sch Syst Engn Reading RG6 2AH Berks England

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection;elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.

关键词： differential evolution operator differential evolutionary algorithm Ultrafast optical techniques Laser beam modulation, pulsing and switching polynomial phase mutation three-point smoothing meta-algorithms mode locking and tuning genetic algorithms genetic algorithm time-domain crossover femtosecond pulse shaping two-point crossover average crossover broadband femtosecond duration laser pulse shaping wavelet operators wavelet transforms Integral transforms Function theory, analysis Optimisation techniques optical pulse shaping waveform matching problem

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Well Quasi Orders in Subclasses of Bounded Treewidth Graphs and Their Algorithmic Applications

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ALGORITHMICA 2012年第1期64卷 3-18页

作者： Fellows, Michael R. Hermelin, Danny Rosamond, Frances A. Max Plank Inst Informat D-66123 Saarbrucken Germany Charles Darwin Univ Sch Engn & Informat Technol Darwin NT 0909 Australia

We show that three subclasses of bounded treewidth graphs are well quasi ordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertex cover are well quasi ordered by the induced subgraph order, graphs with bounded feedback vertex set are well quasi ordered by the topological-minor order, and graphs with bounded circumference are well quasi ordered by the induced minor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.

关键词： Well quasi order Treewidth Tree decomposition Bounded vertex cover graphs Bounded feedback vertex set graphs Bounded circumference graphs Parameterized complexity Exact algorithms meta-algorithms Geometric graph recognition String graphs

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Online Optimization in Cloud Resource Provisioning: Predictions, Regrets, and algorithms

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PROCEEDINGS OF THE ACM ON MEASUREMENT AND ANALYSIS OF COMPUTING SYSTEMS 2019年第1期3卷 1–30页

作者： Comden, Joshua Yao, Sijie Chen, Niangjun Xing, Haipeng Liu, Zhenhua SUNY Stony Brook Dept Appl Math & Stat 100 Nicolls Rd Stony Brook NY 11794 USA Inst High Performance Comp 1 Fusionopolis Way16-16 Connexis North Singapore 138632 Singapore

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.

关键词： online optimization meta-algorithms resource allocation

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A PAC Approach to Application-Specific Algorithm Selection 16

A PAC Approach to Application-Specific Algorithm Selection

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7th ACM Conference on Innovations in Theoretical Computer Science (ITCS)

作者： Gupta, Rishi Roughgarden, Tim Stanford Univ 450 Serra Mall Stanford CA 94305 USA

ISBN: (纸本)9781450340571

The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to selecting the best algorithm for a given application domain, there has been surprisingly little theoretical analysis of the problem. This paper adapts concepts from statistical and online learning theory to reason about application-specific algorithm selection. Our models capture several state-of-theart empirical and theoretical approaches to the problem, ranging from self-improving algorithms to empirical performance models, and our results identify conditions under which these approaches are guaranteed to perform well. We present one framework that models algorithm selection as a statistical learning problem, and our work here shows that dimension notions from statistical learning theory, historically used to measure the complexity of classes of binary-and real-valued functions, are relevant in a much broader algorithmic context. We also study the online version of the algorithm selection problem, and give possibility and impossibility results for the existence of no-regret learning algorithms.

关键词： Algorithm selection Parameter tuning PAC learning Online learning meta-algorithms

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An Optical Character Recognition Approach to Qualifying Thresholding algorithms

An Optical Character Recognition Approach to Qualifying Thre...

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8th ACM Symposium on Document Engineering

作者： Sturgill, Margaret Simske, Steven J. Hewlett Packard Labs Ft Collins CO 80528 USA

ISBN: (纸本)9781605580814

Pre-processing for raster image based document segmentation begins with image thresholding, which is a binarization process separating foreground from background. In this paper, we compare an existing (Otsu), modified existing (Kittler-Illingworth) and simple peak-based thresholding approach on a set of 982 documents for which existing ground truth (full text) is available. We use the Output of all Open Source OCR engine which incorporates an adaptive/dynamic thresholder that can be bypassed by one of the three global thresholds we tested. This allowed comparison of these three approaches in the aggregate. We then used an independently-generated dictionary as a means of characterizing thresholder efficacy. Such an approach, if successful, Will provide the means for selecting an optimal thresholder in the absence of a large set of ground truthed documents. Our preliminary findings here indicate that this approach may provide a reliable means for thresholder comparison and eventually preclude the need for time-intensive human ground truthing.

关键词： Threshold OCR Testing Accuracy Kittler-Illingworth Otsu meta-algorithms

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Online optimization in cloud resource provisioning: Predictions, regrets, and algorithms 19

Online optimization in cloud resource provisioning: Predicti...

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14th Joint Conference of International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2019 and IFIP Performance Conference 2019, SIGMETRICS/Performance 2019

作者： Comden, Joshua Yao, Sijie Chen, Niangjun Liu, Zhenhua Xing, Haipeng Stony Brook University Stony BrookNY United States Institute of High Performance Computing Singapore

ISBN: (纸本)9781450366786

Several different control methods are used in practice or have been proposed to cost-effectively provision IT resources. Due to the dependency of many control methods on having accurate predictions of the future to make good provisioning decisions, there has been a great deal of literature on prediction workload demand. However, even with all of this literature on workload predictions and their utilization in control algorithms, the understanding of prediction error and how to handle it remains an important open issue and research *** this paper we aim to mend this gap by making the following contributions: (i) Prediction error is modeled to aid in proving worst-case dynamic regret bounds for control algorithms. (ii) Upper bounds on dynamic regret are proven for a variety of algorithms in terms of the prediction error model. In order to choose which algorithm to run without prediction error knowledge, a simple online meta-algorithm is designed. (iii) A detailed analysis of prediction accuracy is done for cloud computing by fitting real-world CPU utilization traces of Azure virtual machines to popular prediction models. (iv) Using real-world trace based simulations of CPU allocation for virtual machines, the proposed meta-algorithm is shown to outperform a popular algorithm selection policy and perform very closely to that of the best algorithm chosen in hindsight.

关键词： online optimization resource allocation meta-algorithms

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