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Optimal Bounds for Distinct Quartics 51

Optimal Bounds for Distinct Quartics

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51st International Colloquium on Automata, Languages, and Programming, ICALP 2024

作者： Charalampopoulos, Panagiotis Gawrychowski, Pawel Ghazawi, Samah School of Computing and Mathematical Sciences Birkbeck University of London United Kingdom Institute of Computer Science University of Wroclaw Poland Department of Computer Science University of Haifa Israel Department of Software Engineering Braude College of Engineering Karmiel Israel

ISBN: (纸本)9783959773225

A fundamental concept related to strings is that of repetitions. It has been extensively studied in many versions, from both purely combinatorial and algorithmic angles. One of the most basic questions is how many distinct squares, i.e., distinct strings of the form UU, a string of length n can contain as fragments. It turns out that this is always O(n), and the bound cannot be improved to sublinear in n [Fraenkel and Simpson, JCTA 1998]. Several similar questions about repetitions in strings have been considered, and by now we seem to have a good understanding of their repetitive structure. For higher-dimensional strings, the basic concept of periodicity has been successfully extended and applied to design efficient algorithms – it is inherently more complex than for regular strings. Extending the notion of repetitions and understanding the repetitive structure of higher-dimensional strings is however far from complete. Quartics were introduced by Apostolico and Brimkov [TCS 2000] as analogues of squares in two dimensions. Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020] proved that the number of distinct quartics in an n × n 2D string is O(n2 log2 n) and that they can be computed in O(n2 log2 n) time. Gawrychowski, Ghazawi, and Landau [SPIRE 2021] constructed an infinite family of n × n 2D strings with Ω(n2 log n) distinct quartics. This brings the challenge of determining asymptotically tight bounds. Here, we settle both the combinatorial and the algorithmic aspects of this question: the number of distinct quartics in an n × n 2D string is O(n2 log n) and they can be computed in the worst-case optimal O(n2 log n) time. As expected, our solution heavily exploits the periodic structure implied by occurrences of quartics. However, the two-dimensional nature of the problem introduces some technical challenges. Somewhat surprisingly, we overcome the final challenge for the combinatorial bound using a result of Marcus and Tardos [JCTA 2004] for permuta

关键词： Optimization

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Identifying opportunities for automatic remote field cloning 04

Identifying opportunities for automatic remote field cloning

引用

proceedings of the 2004 conference of the Centre for Advanced Studies on Collaborative research

作者： Christopher Barton Peng Zhao Robert Niewiadomski José Nelson Amaral Department of Computing Science University of Alberta Edmonton Canada

Optimizing compilers can automatically re-arrange data objects to produce memory reference patterns with better reference locality while retaining correct application semantics. This paper describes a new technique, Remote Field Cloning (RFC), that consists of replicating the value from a field of a remote data object. This replication prevents long jumps in the data references of an application. RFC was motivated by work on cache-conscious re-engineering of algorithms. When hand-crafted into suitable algorithms, RFC produces speedups of up to 40% for a well-know refinement-based pathfinding problem. This paper presents a motivating example and a general problem statement of remote field cloning as an optimization problem. A new algorithm that discovers opportunities for RFC is applied to the SPEC2000 benchmark suite and discovers many such opportunities. However a correlation of the percentage of execution time spent in procedures that contain these opportunities reveals that the expected impact of RFC in the SPEC2000 suite is limited.

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Compressed Counting 09

Compressed Counting

引用

Annual acm-Society for Industrial and applied Mathmatics symposium on Discrete Algorithms

作者： Ping Liy Department of Statistical Science Faculty of Computing and Information Science Cornell University

We propose Compressed Counting (CC) for approximating the αth frequency moments (0 < α≤2) of data streams under a relaxed strict-Turnstile model, using maximally-skewed stable random projections. Estimators based on the geometric mean and the harmonic mean are developed. When α = 1, a simple counter suffices for counting the first moment (i.e., sum). The geometric mean estimator of CC has asymptotic variance ∝ Δ = |α-1|, capturing the intuition that the complexity should decrease as Δ=|α-1|→0. However, the previous classical algorithms based on symmetric stable random projections[12, 15] required O(1/ε~2) space, in order to approximate the αth moments within a 1+ε factor, for any 0 < α≤2 including α = 1. We show that using the geometric mean estimator, CC requires O(1/(log (1+ε))+2Δ~(1/2)/((log(1+ε))~(3/2))+o(Δ~(1/2))) space, as Δ→0. Therefore, in the neighborhood of α = 1, the complexity of CC is essentially O (1/ε) instead of O(1/ε~2). CC may be useful for estimating Shannon entropy, which can be approximated by certain functions of the αth moments with α→1. [10, 9] suggested using α = 1+Δ with (e.g.,) Δ< 0:0001 and ε < 10~(-7), to rigorously ensure reasonable approximations. Thus, unfortunately, CC is "theoretically impractical" for estimating Shannon entropy, despite its empirical success reported in [16].

关键词： Geometric mean Moment of force Harmonic mean Intuition COMPRESSED Neighborhood

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Scheduling with relaxed constraint for ATM-like input-queued crossbar switching fabric in IP router

Scheduling with relaxed constraint for ATM-like input-queued...

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Asia-Pacific Conference on Communications

作者： Lixiang Xiong Don Platt Guoqiang Mao School of Electrical and Information Engineering University of Sydney Sydney NSW Australia School of Electrical Computer and Telecommunications Engineering University of Wollongong Wollongong NSW Australia

ISBN: (纸本)0780386019

A scheduling scheme for ATM-like input-queued crossbar switching fabric in the IP router performs a critical role in the IP router. However, there is a problem among the existing scheduling schemes: when an IP router with a large number of outputs (e.g. 64, 128 or more) is connected to only a few nodes (e.g. 2 or 4 nodes, where the node may be another IP router or a switch), the switching capability is not fully utilized. We propose an approach to improve the existing scheduling schemes: all outputs of the switching fabric are divided into a few groups whose number is equal to the number of nodes to be connected, and outputs in the same group are multiplexed into a high-speed output link which is connected to a node. Therefore all outputs of the switching fabric can join the switching. The approach is applied to several popularly used scheduling algorithms. Simulation is carried out to demonstrate a better performance.

关键词： Fabrics Round robin Switches Telecommunication switching Australia Packet switching Communication switching Telecommunication computing Processor scheduling Scheduling algorithm

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An assessment of eLearning technologies to support telecommunications laboratory learning objectives

An assessment of eLearning technologies to support telecommu...

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Annual Hawaii International Conference on System Sciences (HICSS)

作者： J. Lucca N.C. Romano R. Sharda M. Weiser Oklahoma State University USA

While current distance learning (DL), now sometimes referred to as "eLearning", technologies focus on bringing the classroom to a remote student, the next generation of eLearning, has the potential to bring remote students into the laboratory. Virtual reality systems are being developed to engage the user as fully as possible within a computer-supported environment. This paper describes an on-going implementation of an environment that allows remote interaction with equipment and other participants that previously required co-location. Technology is used to extend a telecommunications laboratory (lab) to enable acquisition of cognitive, affective and psychomotor skills. New hardware and software are being applied to develop a virtual lab experience through which remote students can attain learning objectives as well as students that use a traditional face-to-face (F2F) lab environment. A same-time/different-place (STDP) learning environment can be both a cost effective and convenient way to educate students. The design, development, and assessment of such a system is presented.

关键词： Electronic learning Laboratories Psychology Collaborative work Computer aided instruction Computer interfaces DSL Virtual reality Telecommunication computing Hardware

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From facial expression to level of interest: a spatio-temporal approach

From facial expression to level of interest: a spatio-tempor...

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： M. Yeasin B. Bullot R. Sharma Computer Science Institute of Technology State University of New York USA Computer Science and Engineering Pennsylvania State University USA

This paper presents a novel approach to recognize the six universal facial expressions from visual data and use them to derive the level of interest using psychological evidences. The proposed approach relies on a two-step classification built on the top of refined optical flow computed from sequence of images. First, a bank of linear classifier was applied at frame level and the output of this stage was coalesced to produce a temporal signature for each observation. Second, temporal signatures thus computed from the training data set were used to train discrete hidden Markov models (HMMs) to learn the underlying models for each universal facial expressions. The average recognition rate of the proposed facial expression classifier is 90.9% without classifier fusion and 91.2% with fusion using a five fold cross validation scheme on a database of 488 video sequences that include 97 subjects. Recognized facial expressions were combined with the intensity of activity (motion) around the apex frame to measure the level of interest. To further illustrate the efficacy of the proposed approach two set of experiments, namely, television (TV) broadcast data (108 sequences of facial expression containing severe lighting conditions, diverse subjects and expressions) analysis and emotion elicitation on 21 subjects were conducted.

关键词： Face recognition Hidden Markov models Optical computing TV Psychology Image motion analysis Training data Databases Video sequences Motion measurement

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Inferring Regulatory Interactions between Transcriptional Factors and Genes by Propagating Known Regulatory Links

Inferring Regulatory Interactions between Transcriptional Fa...

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IEEE symposium on Computational Intelligence and Bioinformatics and Computational Biology (CIBCB)

作者： Qian Zhong Riccardo Boscolo Timothy S. Gardner Vwani P. Roychowdhury Department of Electrical Engineering University of California Los Angeles CA USA Center for BioDynamics and Department of Biomedical Engineering Boston University Boston MA USA

Determining transcriptional regulatory networks has been one of the most important goals in the field of functional genomics. Despite the recent advances in experimental techniques, complementary computational techniques have lagged behind. We introduce a novel computational methodology that uses DNA microarray data and known regulatory interactions to predict unknown regulatory interactions. Our method involves three steps: in the training stage, we utilize network component analysis (NCA) (Liao et al., 2003; Kao et al., 2004; Boscolo et al., 2005) to reconstruct the hidden activity profiles of transcriptional factors (TF); then we cluster TFs into functional modules according to the similarities of their reconstructed activity profiles; in the prediction stage, we infer additional TF-gene regulatory links by selecting TF profiles that best interpret genes expression profiles via a linear model. We applied the methodology to a gene expression dataset of bacterium Escherichia coli, whose partial TF-gene regulatory structure is obtained from RegulonDB (Salgado et al., 2004). Cross-validation results show that when the profiles of all TFs regulating a gene are reconstructed from NCA, we could identify 36% of the TF-gene interactions, and the prediction accuracy is 89%. And when the profiles of partial (50% or more) TFs regulating a gene can be reconstructed, we can identify 14% of the TF-gene interactions, and the accuracy rate is 69%. These represent some of the best known accuracy and coverage statistics reported in the literature so far

关键词： Bioinformatics Genetic expression Genomics Predictive models USA Councils Biomedical computing DNA computing Statistics Computational intelligence Computational biology

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Compression of samplable sources

Compression of samplable sources

引用

Annual IEEE Conference on Computational Complexity

作者： L. Trevisan S. Vadhan D. Zuckerman Computer Science Division University of California Berkeley Berkeley CA USA Division of Engineering & Applied Sciences Harvard University Cambridge MA USA Department of Computer Science University of Technology Austin TX USA

We study the compression of polynomially samplable sources. In particular, we give efficient prefix-free compression and decompression algorithms for three classes of such sources (whose support is a subset of {0, l}/sup n/). 1) We show how to compress sources X samplable by logspace machines to expected length H(X) + O(1). Our next results concern flat sources whose support is in P. 2) If H(X) /spl les/ k = n - O(log n), we show how to compress to length k + /spl delta//spl middot/ (n - k) for any constant /spl delta/ > 0; in quasi-polynomial time we show how to compress to length k + O(polylog log (n - k)) even if k = n -polylog(n). 3) If the support of X is the witness set for a self-reducible NP relation, then we show how to compress to expected length H(X) + 4.

关键词： Polynomials Sampling methods Computer science Data compression Stochastic processes Distributed computing Compression algorithms Information theory Random variables Entropy

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computing equilibria for congestion games with (im)perfect information 04

Computing equilibria for congestion games with (im)perfect i...

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proceedings of the fifteenth annual acm-SIAM symposium on Discrete algorithms

作者： Rene Beier Artur Czumaj Piotr Krysta Berthold Vöcking Max-Planck-Institut für Informatik Saarbruecken Germany New Jersey Institute of Technology Newark NJ Dortmund University Dortmund Germany

ISBN: (纸本)9780898715583

We study algorithmic questions concerning a basic microeconomic congestion game in which there is a single provider that offers a service to a set of potential customers. Each customer has a particular demand of service and the behavior of the customers is determined by utility functions that are non-increasing in the congestion. Customers decide whether to join or leave the service based on the experienced congestion and the offered prices. Following standard game theory, we assume each customer behaves in the most rational way. If the prices of service are fixed, then such a customer behavior leads to a pure, not necessarily unique Nash equilibrium among the customers. In order to evaluate marketing strategies, the service provider is interested in estimating its revenue under the best and worst customer equilibria. We study the complexity of this problem under different models of information available to the provider.•We first consider the classical model in which the provider has perfect knowledge of the behavior of all customers. We present a complete characterization of the complexity of computing optimal pricing strategies and of computing best and worst equilibria. Basically, we show that most of these problems are inapproximable in the worst case but admit an "average-case FPAS." Our average case analysis covers general distributions for customer demands and utility thresholds. We generalize our analysis to robust equilibria in which players change their strategies only when this promises a significant utility improvement.•We extend our analysis to a more realistic model in which the provider has incomplete information. Following the game theoretic framework of Bayesian games introduced by Harsanyi, we assume that the provider is aware of probability distributions describing the behavior of the customers and aims at estimating its expected revenue under best and worst equilibria. Somewhat counterintuitive, we obtain an FPRAS for the equilibria problem in th

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Amplitude spectrum-based gait recognition

Amplitude spectrum-based gait recognition

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International Conference on Automatic Face and Gesture Recognition

作者： Guoying Zhao Rui Chen Guoyi Liu Hua Li Graduate School of Chinese Academy of Sciences Beijing China Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy and Sciences Beijing China

ISBN: (纸本)0769521223

Gait is a biometric feature and identification of people from gait captured on video that has become a challenging problem in computer vision. A recognition method based on amplitude spectrum (Fourier spectrum) of frequency domain is proposed. Fourier spectrum reflects the frequency feature of person's pose in the current frame. After getting the period and key poses through the whole sequence according to the height of centroid and the amplitude value in frequency domain, we extract 5D features from the sequence including four amplitude values corresponding to four key poses image and the proportion of body. Finally, three measures are applied to evaluate our algorithm. Experiments result on USF dataset show that our method is insensitive to many changes condition of background, lighting, clothing, walking speed, segment noise and so on. For we implement gait recognition according to the discriminant analysis, the result to some extent is robust to the variation of viewpoint and cloth and recognition rate is satisfying.

关键词： Biometrics Face recognition Image recognition Frequency domain analysis Clothing Legged locomotion Iris Fingerprint recognition Humans Surveillance

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