Streaming Algorithm Research Articles

Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time

We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than 2 . Specifically, we obtain a \(1+\tfrac{1}{\sqrt {2}}+\epsilon \approx 1.707+\epsilon\) approximation in bipartite graphs and a \(1.973+\epsilon\) approximation in general graphs. We thus answer in the affirmative the value version of the major open question repeatedly asked in the dynamic graph algorithms literature. Our randomized algorithms’ approximation and worst-case update time bounds both hold w.h.p. against adaptive adversaries. Our algorithms are based on simulating new two-pass streaming matching algorithms in the dynamic setting. Our key new idea is to invoke the recent sublinear-time matching algorithm of Behnezhad (FOCS’21) in a white-box manner to efficiently simulate the second pass of our streaming algorithms, while bypassing the well-known vertex-update barrier.

A Hybrid System Based on Three Levels to Hide Information using JPEG Color Images

Nowadays, due to the circulation of information among people, information security has become an important requirement to protect information from hacking. Many techniques have been discovered to protect this information and maintain its confidentiality from hacking, the most prominent of which are cryptography and steganography techniques. In this paper, a hybrid system based on three levels to hide information using Joint Photographic Experts Group (JPEG) color images, where this system works in both processes sender and receiver. The sender process at the first level uses a mixing of the Advanced Encryption Standard (AES) and Rivest Shamir Adleman (RSA), while at the second level uses a Fuzzy Stream Algorithm (FSA) adds a higher complexity and eliminates the non-linearity of the encrypted information. The third level is to hide encrypted information using the Least Significant Bit (LSB) technique, while the receiver process, performs the reverse process of three levels. This system provides high information embedding capability and the inability to perceive hidden information, the system was evaluated based on criteria like Peak Signal Noise Ratio (PSNR), Mean Square Error (MSE), Structure Similarity (SSIM), and correlation, which were characterized by high and good rates. The study was compared with modern steganography techniques.

A quantum algorithm for the lattice-Boltzmann method advection-diffusion equation

We present a versatile and efficient quantum algorithm based on the Lattice Boltzmann method (LBM) approximate solution of the linear advection-diffusion equation (ADE). We emphasize that the LBM approximation modifies the diffusion term of the underlying exact ADE and leads to a modified equation (mADE). Due to its versatility in terms of operator splitting, the proposed quantum LBM algorithm for the mADE provides a building block for future quantum algorithms to solve the linearized Navier-Stokes equation on quantum computers. We split the algorithm into four operations: initialization, collision, streaming, and calculation of the macroscopic quantities. We propose general quantum building blocks for each operator, which adapt intrinsically from the general three-dimensional case to smaller dimensions and apply to arbitrary lattice-velocity sets. Based on (sub-linear) amplitude data encoding, we propose improved initialization and collision operations with reduced complexity and efficient sampling-based simulation. Quantum streaming algorithms are based on previous developments. The proposed quantum algorithm allows for the computation of successive time steps, requiring full state measurement and reinitialization after every time step. It is validated by comparison with a digital implementation and based on analytical solutions in one and two dimensions. Furthermore, we demonstrate the versatility of the quantum algorithm for two cases with non-uniform advection velocities in two and three dimensions. Various velocity sets are considered to further highlight the flexibility of the algorithm. We benchmark our optimized quantum algorithm against previous methods employed in sampling-based quantum simulators. We demonstrate sampling efficiency, with sampling accelerated convergence requiring fewer shots.

A Framework for Adversarial Streaming Via Differential Privacy and Difference Estimators

Classical streaming algorithms operate under the (not always reasonable) assumption that the input stream is fixed in advance. Recently, there is a growing interest in designing robust streaming algorithms that provide provable guarantees even when the input stream is chosen adaptively as the execution progresses. We propose a new framework for robust streaming that combines techniques from two recently suggested frameworks by Hassidim et al. (NeurIPS 2020) and by Woodruff and Zhou (FOCS 2021). These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks into a single hybrid framework that obtains the “best of both worlds”, thereby solving a question left open by Woodruff and Zhou.

Streaming Algorithms for Geometric Steiner Forest

We consider a generalization of the Steiner tree problem, the Steiner forest problem , in the Euclidean plane: the input is a multiset \(X\subseteq{\mathbb{R}}^{2}\) , partitioned into \(k\) color classes \(C_{1},\ldots,C_{k}\subseteq X\) . The goal is to find a minimum-cost Euclidean graph \(G\) such that every color class \(C_{i}\) is connected in \(G\) . We study this Steiner forest problem in the streaming setting, where the stream consists of insertions and deletions of points to \(X\) . Each input point \(x {\in} X\) arrives with its color \(\mathsf{color}(x) {\in} [k]\) , and as usual for dynamic geometric streams, the input is restricted to the discrete grid \(\{1,\ldots,\Delta\}^{2}\) . We design a single-pass streaming algorithm that uses \(\operatorname{poly}(k\cdot\log\Delta)\) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio \(\alpha_{2}\) (currently \(1.1547\leq\alpha_{2}\leq 1.214\) ). This approximation guarantee matches the state-of-the-art bound for streaming Steiner tree, i.e., when \(k=1\) , and it is a major open question to improve the ratio to \(1+\varepsilon\) even for this special case. Our approach relies on a novel combination of streaming techniques, like sampling and linear sketching, with the classical Arora-style dynamic-programming framework for geometric optimization problems, which usually requires large memory and so far has not been applied in the streaming setting. We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite multiplicative approximation requires \(\Omega(k)\) bits of space.

An online ensemble classification algorithm for multi-class imbalanced data stream

An online ensemble classification algorithm for multi-class imbalanced data stream

Fast bicriteria streaming algorithms for submodular cover problem under noise models

The Submodular Cover (SC) problem has attracted the attention of researchers because of its wide variety of applications in many domains. Previous studies on this problem have focused on solving it under the assumption of a non-noise environment or using the greedy algorithm to solve it under noise. However, in some applications, the data is often large-scale and brings a noisy version, so the existing solutions are ineffective or not applicable to large and noisy data. Motivated by this phenomenon, we study the Submodular Cover under Noises (SCN) problem and propose two efficient streaming algorithms, which provide a solution with theoretical bounds under two common noise models, multiplicative and additive noises. The experimental results indicate that our proposed algorithms not only provide the solution with a high objective function value but also outperform the state-of-the-art algorithm in terms of both the number of queries and the running time.

Towards Metric DBSCAN: Exact, Approximate, and Streaming Algorithms

DBSCAN is a popular density-based clustering algorithm that has many different applications in practice. However, the running time of DBSCAN in high-dimensional space or general metric space (\em e.g., clustering a set of texts by using edit distance) can be as large as quadratic in the input size. Moreover, most of existing accelerating techniques for DBSCAN are only available for low-dimensional Euclidean space. In this paper, we study the DBSCAN problem under the assumption that the inliers (the core points and border points) have a low intrinsic dimension (which is a realistic assumption for many high-dimensional applications), where the outliers can locate anywhere in the space without any assumption. First, we propose a k-center clustering based algorithm that can reduce the time-consuming labeling and merging tasks of DBSCAN to be linear. Further, we propose a linear time approximate DBSCAN algorithm, where the key idea is building a novel small-size summary for the core points. Also, our algorithm can be efficiently implemented for streaming data and the required memory is independent of the input size. Finally, we conduct our experiments and compare our algorithms with several popular DBSCAN algorithms. The experimental results suggest that our proposed approach can significantly reduce the computational complexity in practice.

Streaming Algorithms with Few State Changes

In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these metrics fail to capture the asymmetric costs, inherent in modern hardware and database systems, of reading versus writing to memory. In fact, most streaming algorithms write to their memory on every update, which is undesirable when writing is significantly more expensive than reading. This raises the question of whether streaming algorithms with small space and number of memory writes are possible. We first demonstrate that, for the fundamental F p moment estimation problem with p ≥ 1, any streaming algorithm that achieves a constant factor approximation must make Ω(n 1-1/p ) internal state changes, regardless of how much space it uses. Perhaps surprisingly, we show that this lower bound can be matched by an algorithm which also has near-optimal space complexity. Specifically, we give a (1+ε)-approximation algorithm for F p moment estimation that use a near-optimal ~O ε (n 1-1/p ) number of state changes, while simultaneously achieving near-optimal space, i.e., for p∈[1,2), our algorithm uses poly(log n,1/ε) bits of space for, while for p>2, the algorithm uses ~O ε (n 1-1/p ) space. We similarly design streaming algorithms that are simultaneously near-optimal in both space complexity and the number of state changes for the heavy-hitters problem, sparse support recovery, and entropy estimation. Our results demonstrate that an optimal number of state changes can be achieved without sacrificing space complexity.

Sketching Approximability of All Finite CSPs

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k . An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q = k =2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [ 47 ] and [ 41 ], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [ 56 ], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q -ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes.

Constructive Separations and Their Consequences

For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the questions: Which lower bounds can be made constructive? What are the consequences of constructive separations? We build a case that "constructiveness" serves as a dividing line between many weak lower bounds we know how to prove, and strong lower bounds against $P$, $ZPP$, and $BPP$. Put another way, constructiveness is the opposite of a complexity barrier: it is a property we want lower bounds to have. Our results fall into three broad categories. 1. Our first set of results shows that, for many well-known lower bounds against streaming algorithms, one-tape Turing machines, and query complexity, as well as lower bounds for the Minimum Circuit Size Problem, making these lower bounds constructive would imply breakthrough separations ranging from $EXP \neq BPP$ to even $P \neq NP$. 2. Our second set of results shows that for most major open problems in lower bounds against $P$, $ZPP$, and $BPP$, including $P \neq NP$, $P \neq PSPACE$, $P \neq PP$, $ZPP \neq EXP$, and $BPP \neq NEXP$, any proof of the separation would further imply a constructive separation. Our results generalize earlier results for $P \neq NP$ [Gutfreund, Shaltiel, and Ta-Shma, CCC 2005] and $BPP \neq NEXP$ [Dolev, Fandina and Gutfreund, CIAC 2013]. 3. Our third set of results shows that certain complexity separations cannot be made constructive. We observe that for all super-polynomially growing functions $t$, there are no constructive separations for detecting high $t$-time Kolmogorov complexity (a task which is known to be not in $P$) from any complexity class, unconditionally.

Design and implementation for a UAV-based streaming media system

The Unmanned Aerial Vehicle (UAV)-based video streaming transmission is critical for real-time communication (RTC) applications in flying ad-hoc networks (FANET). The communication links between the nodes, however, are often unstable, especially in harsh network environments. This article first presents an architecture of a UAV-based streaming media system (USMS) for more reliable transmission, where the UAVs play multiple roles simultaneously in terms of video capturing, encoding, transmission, caching, decoding, and evaluation. To promote fluency of video transmission, we propose a distributed algorithm to explore the Tradeoff between the bandWidth, the Load, and the Video parameters (TWLV) based on the UAV flying status and Quality of Service (QoS). To enhance the Quality of Experience (QoE) significantly, we design an application-oriented multi-link transmission system with a novel multi-module stacking technology. Leveraging this design, we implement an extended splitting-merging streaming (ESMS) algorithm to deal with heavy payloads and reduce transmission latency. We also propose a multi-link retransmission (MLR) algorithm to eliminate consecutive packet losses and achieve more efficient video rebuffering. Sufficient experimental results verify that compared with the commercially available products that utilize application-layer forward error correction (AL-FEC), MultiPath TCP (MPTCP), and Deadline-aware Transport Protocol (DTP), our proposed USMS outperforms in throughput promotion, latency reduction, congestion control, packet recovery, and rebuffering efficiency.

Multipass Streaming Algorithms for Regularized Submodular Maximization

Multipass Streaming Algorithms for Regularized Submodular Maximization

Efficient Online Stream Clustering Based on Fast Peeling of Boundary Micro-Cluster.

A growing number of applications generate streaming data, making data stream mining a popular research topic. Classification-based streaming algorithms require pre-training on labeled data. Manually labeling a large number of samples in the data stream is impractical and cost-prohibitive. Stream clustering algorithms rely on unsupervised learning. They have been widely studied for their ability to effectively analyze high-speed data streams without prior knowledge. Stream clustering plays a key role in data stream mining. Currently, most data stream clustering algorithms adopt the online-offline framework. In the online stage, micro-clusters are maintained, and in the offline stage, they are clustered using an algorithm similar to density-based spatial clustering of applications with noise (DBSCAN). When data streams have clusters with varying densities and ambiguous boundaries, traditional data stream clustering algorithms may be less effective. To overcome the above limitations, this article proposes a fully online stream clustering algorithm called fast boundary peeling stream clustering (FBPStream). First, FBPStream defines a decay-based kernel density estimation (KDE). It can discover clusters with varying densities and identify the evolving trend of streams well. Then, FBPStream implements an efficient boundary micro-cluster peeling technique to identify the potential core micro-clusters. Finally, FBPStream employs a parallel clustering strategy to effectively cluster core and boundary micro-clusters. The proposed algorithm is compared with ten popular algorithms on 15 data streams. Experimental results show that FBPStream is competitive with the other ten popular algorithms.

Streaming Algorithms for Non-Submodular Maximization on the Integer Lattice

Many practical problems emphasize the importance of not only knowing whether an element is selected but also deciding to what extent it is selected, which imposes a challenge on submodule optimization. In this study, we consider the monotone, nondecreasing, and non-submodular maximization on the integer lattice with a cardinality constraint. We first design a two-pass streaming algorithm by refining the estimation interval of the optimal value. For each element, the algorithm not only decides whether to save the element but also gives the number of reservations. Then, we introduce the binary search as a subroutine to reduce the time complexity. Next, we obtain a one-pass streaming algorithm by dynamically updating the estimation interval of optimal value. Finally, we improve the memory complexity of this algorithm.

A hybrid lattice Boltzmann method for gaseous detonations

This article is dedicated to the construction of a robust and accurate numerical scheme based on the lattice Boltzmann method (LBM) for simulations of gaseous detonations. This objective is achieved through careful construction of a fully conservative hybrid lattice Boltzmann scheme tailored for multi-species reactive flows. The core concept is to retain LBM low dissipation properties for acoustic and vortical modes by using the collide and stream algorithm for the particle distribution function, while transporting entropic and species modes via a specifically designed finite-volume scheme. The proposed method is first evaluated on common academic cases, demonstrating its ability to accurately simulate multi-species compressible and reactive flows with discontinuities: the convection of inert species, a Sod shock tube with two ideal gases and a steady one-dimensional inviscid detonation wave. Subsequently, the potential of this novel approach is demonstrated in one- and two-dimensional inviscid unsteady gaseous detonations, highlighting its ability to accurately recover detonation structures and associated instabilities for high activation energies. To the authors' knowledge, this study is the first successful simulation of detonation cellular structures capitalizing on the LBM collide and stream algorithm.

Small Vertex Cover Helps in Fixed-Parameter Tractability of Graph Deletion Problems over Data Streams

In the study of parameterized streaming complexity on graph problems, the main goal is to design streaming algorithms for parameterized problems such that O(f(k)logO(1)n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(f(k) \\log ^{\\mathcal {O}(1)} n)$$\\end{document} space is enough, where f is an arbitrary computable function depending only on the parameter k. However, in the past few years very few positive results have been established. Most of the graph problems that do have streaming algorithms of the above nature are ones where localized checking is required, like Vertex Cover or Maximum Matching parameterized by the size k of the solution we are seeking. Chitnis et al. (SODA’16) have shown that many important parameterized problems that form the backbone of traditional parameterized complexity are known to require Ω(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega (n)$$\\end{document} bits of storage for any streaming algorithm; e.g. Feedback Vertex Set, Even Cycle Transversal, Odd Cycle Transversal, Triangle Deletion or the more general F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{F}$$\\end{document}-Subgraph Deletion when parameterized by solution size k. Our contribution lies in overcoming the obstacles to efficient parameterized streaming algorithms in graph deletion problems by utilizing the power of parameterization. We focus on the vertex cover size K as the parameter for the parameterized graph deletion problems we consider. In this work, we consider the four most well-studied streaming models: the Ea, Dea, Va (vertex arrival) and Al (adjacency list) models. Surprisingly, the consideration of vertex cover size K in the different models leads to a classification of positive and negative results for problems like F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{F}$$\\end{document}-Subgraph Deletion and F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{F}$$\\end{document}-Minor Deletion.

Steel Surface Defect Detection Based on SSAM-YOLO

The defect inspection of the steel surface is crucial to modern manufacturing and highly depends on inefficient manual work. The emergence of deep learning has prompted the development of automated defect detection methods, but the current methods perform badly in the detection of the crazing and rolled-in scale-two types of defects on steel surfaces. The difficulty in the detection of crazing and rolled-in scale is mainly due to the similarity between object regions and background regions. Based on this, the authors propose a supervised spatial-attention module (SSAM). It introduces a priori knowledge compared to the traditional spatial attention mechanism, which can enhance the supervision of relevant parameters in the attention mechanism module during network training. Finally, they introduced the SSAM to the YOLOv5 and got the SSAM-YOLO. The test result on the NEU-DET dataset shows that the proposed method has better detection accuracy, achieving improvements of 7.3% and 3.02% on the AP@0.5 for the crazing and rolled-in scale. The method also outperforms the comparative main stream algorithms for steel surface defect detection, verifying the effectiveness of our algorithm.

Adaptive Video Streaming With Automatic Quality-of-Experience Optimization

Video streaming has grown tremendously in recent years and it is now one of the main applications on the Internet. Due to the networks' inherent bandwidth fluctuations, various rate-adaptive streaming algorithms have been developed to compensate for such fluctuations to improve Quality-of-Experience (QoE). However, in practice, the preference for QoE typically differs significantly across different viewers and there is no systematic way so far to comprehensively incorporate different sets of conflicting QoE objectives into the algorithm design. Thus, it is not surprising that the QoE performance achieved by the existing algorithms is in fact far from optimal. This work aims at attacking the heart of the problem by developing a novel framework called Post Streaming Quality Analysis (PSQA) that can maximize the QoE under any preference through automatically tuning the adaptation logic of the streaming algorithms. Evaluation results show that the QoE achieved by PSQA is substantially better than the existing approaches and in some scenarios even close to optimal. Moreover, PSQA can be readily implemented into real streaming platforms, offering a practical and reliable solution for high-performance streaming services.

Streaming Algorithms for Non-Submodular Functions Maximization with d-Knapsack Constraint on the Integer Lattice

We study the problem of maximizing a monotone non-submodular function under a [Formula: see text]-knapsack constraint on the integer lattice. We propose three streaming algorithms to approach this problem. We first design a two-pass [Formula: see text]-approximate algorithm with total memory complexity [Formula: see text], and total query complexity for each element [Formula: see text]. The algorithm relies on a binary search technique to determine the amount of the current elements to be added into the output solution. It also requires to have a good estimate of the optimal value, we use the maximum value of the unit standard vector which can be obtained by reading a round of data to construct a guess set of the optimal value. Then, we modify our algorithm to avoid a repetitive reading of data by dynamically update the maximum value of the unit vector along with the coming elements, and obtain a one-pass streaming algorithm with same approximate ratio. Moreover, we design an improved StreamingKnapsack algorithm to reduce the memory complexity to [Formula: see text].