Detecting periodic burst (PB) items in data streams is crucial for applications like rate limiting but remains unexplored. % While combining existing sketch algorithms offers a baseline, it suffers from significant inaccuracy and inefficiency. In this paper, we propose PBSketch, the first dedicated sketch algorithm designed for detecting PB items in real time. Its key techniques mainly include: 1) a two-stage hierarchical structure that efficiently maintains potential burst items and discards those without potential; 2) a fine-grained PB selection mechanism during window processing, coupled with the Window Smoothing Processing optimization to amortize performance overhead and eliminate processing spikes. % We provide its error bounds through rigorous theoretical analysis. Our extensive experiments show that PBSketch outperforms the baseline solution in accuracy and speed. By deploying it on an FPGA platform, the throughput is further significantly improved. Moreover, it effectively optimizes a practical application of rate limiting, clearly improving performance with almost negligible overhead.

In the modern internet, with the proliferation of real-time applications such as online gaming and video conferencing, the timely detection of network jitter has become a critical task in network measurement. Network jitter is defined as the abrupt fluctuations in packet inter-arrival times within network flows, which severely degrade the Quality of Service for these applications. Traditional jitter detection methods primarily focus on macro-level end-to-end or hop-by-hop latency variations, neglecting the fine-grained jitter that occurs within specific flows. In this paper, we present JitterSketch, the first sketch-based algorithm specifically designed for detecting jittery flows. JitterSketch employs a novel three-stage structure to efficiently filter out infrequent and stable flows, thereby identifying and reporting the jittery flows that have the most significant impact on network quality. Extensive experiments demonstrate that JitterSketch achieves an improvement of up to 50 percentage points in both recall and precision rates compared to baseline solutions, while maintaining high processing throughput. Furthermore, we deployed JitterSketch in a QoS simulation system, where it yielded significant improvements in QoS.

Efficient data stream processing, particularly for persistence estimation, is crucial in handling high-velocity data streams characterized by skewed distributions of item frequencies. Unlike more straightforward frequency metrics, persistence captures items' recurrence across multiple time windows, posing a significant challenge to existing single-structure sketches where high-persistence and low-persistence items collide. To address this, we introduce the Hypersistent Sketch, a unified framework for high-performance estimation built on two decoupled mechanisms: filtering and accelerating. The filtering component, a Cold Filter, directly addresses the skewed nature of data streams. It separates hot items from the majority of cold ones, which allows for differential treatment. The accelerating component, a Burst Filter, then optimizes the processing of hot items. It significantly improves throughput by preventing repeated insertions within a single window. We demonstrate its generality by applying it to various state-of-the-art sketches (e.g., On-Off, Waving, P-Sketch), showing it consistently enhances their original performance. We also deploy our framework on Redis platforms, demonstrating the framework’s broad applicability and scalability.

Graphs play an increasingly important role in various big data applications. However, existing graph data structures cannot simultaneously address the performance bottlenecks caused by the dynamic updates, large scale, and high query complexity of current graphs. This paper proposes a novel data structure for large-scale dynamic graphs called CuckooGraph. It does not require any prior knowledge of the upcoming graphs, and can adaptively resize to the most memory-efficient form while requiring few memory accesses for very fast graph data processing. The key techniques of CuckooGraph include TRANSFORMATION and DENYLIST. TRANSFORMATION fully utilizes the limited memory by designing related data structures that allow flexible space transformations to smoothly expand/tighten the required space depending on the number of incoming items. DENYLIST efficiently handles item insertion failures and further improves processing speed. Our experimental results show that compared with the most competitive solution Spruce, Cuckoo-Graph achieves about 33× higher insertion throughput while requiring only about 68% of the memory space.

Graph stream is a special kind of data stream, where every item coming in sequence represents an edge in a dynamic graph. Graph stream has wide application in many fields, including cyber security, social networks and financial fraud detection. In this paper, we propose HourglassSketch, a two-stage data structure, for high-accuracy graph stream summarization. In Stage 1, HourglassSketch uses a CocoSketch to accurately record a partial collection of large-weight edges. In Stage 2, HourglassSketch integrates a TowerSketch with a TCMSketch to approximately record the statistics of most small-weight edges. In addition, we propose a key technique named Error Funnel to further reduce its error margin. Theoretical analysis and experimental results demonstrate that HourglassSketch supports various kinds of query operation and adapts well to graph stream storage. HourglassSketch achieves up to 100x smaller error and 2.7x higher speed than prior work. We also explore the versatility of HourglassSketch as a hardware-friendly framework by implementing it on FPGA and P4 platforms. We have released our codes on GitHub.

Perfect hashing is a special hashing function that maps each item to a unique location without collision, which enables the creation of a KV store with small and constant lookup time. Recent dynamic perfect hashing attains high load factor by increasing associativity, which impacts bandwidth and throughput. This paper proposes a novel dynamic perfect hashing index without sacrificing associativity, and uses it to devise an RDMA-based remote memory KV store called CuckooDuo. CuckooDuo simultaneously achieves high load factor, fast speed, minimal bandwidth, and efficient expansion without item movement. We theoretically analyze the properties of CuckooDuo, and implement it in an RDMA-network based testbed. The results show CuckooDuo achieves 1.9~17.6x smaller insertion latency and 9.0~18.5x smaller insertion bandwidth than prior works.

Sketching algorithms are considered as promising solutions for approximate query tasks on large volumes of data streams. An ideal general-purpose data processing engine requires a sketch to achieve (1) high genericness in supporting a broad range of query tasks; (2) highfidelity in providing accuracy guarantee; and (3) high performance in practice. Although the universal sketch achieves high genericness and fidelity, its accuracy falls short of expectations. In this paper, we propose LETFramework (short for Lossless ExTraction Framework) to optimize the performance of the universal sketch. With the key technique of lossless extraction, LETFramework losslessly extracts the main body of the frequent items and stores the remaining information in the universal sketch, thereby achieving higher accuracy while maintaining high fidelity. We further introduce a unified methodology to incorporate the substitution strategies from top-k algorithms into LETFramework. Experiment results show that, LETFramework outperforms the universal sketch, achieving accuracy improvements ranging from 1 to 3 orders of magnitude on most query tasks and up to 15.73 times higher throughput. All the related source code is open-sourced and available at Github.

Set measurements are fundamental in numerous areas including network measurement, database queries, and data mining. These measurements are typically executed on multisets. Existing algorithms optimize a specific set measurement task, leading to sophisticated but narrowly focused solutions. This specialization often results in inefficiencies when multiple set measurement tasks are required simultaneously, consuming excessive computational and storage resources. This paper introduces DaVinci Sketch, a versatile sketch designed to efficiently handle various set measurement tasks using a single unified data structure. DaVinci Sketch employs a novel approach by utilizing a dedicated structure to store frequent elements, thereby reducing collisions among flows that have the most significant impact on results. Remarkably, DaVinci Sketch can simultaneously perform up to nine different measurement tasks with a single data structure and a unified operation, whereas other approaches typically support fewer tasks. The experimental results demonstrate that DaVinci Sketch achieves high accuracy across 9 measurement tasks. Furthermore, in multi-task scenarios, DaVinci Sketch significantly reduces the memory usage (by more than 59%) and achieves high throughput (more than 23 times faster than other methods).

This paper studies an unexplored attribute in data streams - item freshness. The freshness of an item refers to the time interval between its last arrival and the present moment. The information of item freshness is useful in various scenarios like cache, online advertising, computer network, etc. Currently, there is no algorithm tailored for estimating item freshness. We propose a theoretically guaranteed sketch algorithm called RingSketch, which integrates time-agnostic sketch algorithm with time-aware CLOCK algorithm for real-time freshness measurement. With the key idea of tracing the trajectory of the clock pointer, the estimation process of RingSketch is akin to observing the length of the growth rings in a tree trunk. We theoretically derive the average error of RingSketch and validate it with extensive experiments. The results show that RingSketch simultaneously achieves high accuracy (<10-3 average relative error) and fast update speed (>11.4 M/s), outperforming the baseline solutions by at least 13.3x and 1.5x respectively. All codes are open-sourced at GitHub.

In recent years, sketching has emerged as a pivotal technique for identifying heavy hitters (items with high frequency) in large-scale data streams. Despite this progress, the majority of existing sketch algorithms are tailored primarily for detecting local heavy hitters within a single data stream, with only a few capable of extending their application to global heavy hitters across distributed data streams. A common challenge encountered by these algorithms is balancing performance with accuracy. To address this challenge, we introduce HeavyLocker, a novel sketch algorithm that takes advantage of a distinct feature of real data streams: the separability of heavy hitters. By leveraging this attribute, HeavyLocker precisely locks and protects potential heavy hitters during the data stream processing, ensuring accuracy in local heavy hitter detection without compromising on speed. This unique capability also facilitates its application to global detection tasks. Through theoretical analysis, we validate the efficacy of HeavyLocker's locking mechanism. Our extensive experiments show that HeavyLocker outperforms five benchmarked algorithms in accuracy and maintains fast speed for both local and global heavy hitter detection, significantly reducing errors by up to an order of magnitude compared to the renowned Double-Anonymous Sketch.

The advanced capabilities of Large Language Models (LLMs) have inspired the development of various interactive web services or applications, such as ChatGPT, which offer query inference services for users. Unlike traditional DNN model, the inference of LLM entails different iterations of forward computation for different queries, which result in efficiency challenges for existing run-to-completion batch-wise inference. Hence, some methods refine batch-wise inference to iteration-level by duplicating all nonlinear layers of LLM. However, this approach not only increases resource usage but also introduces idle computations to the batch due to the prefilling of newly added queries. Therefore, we propose BATON, an efficient batch-wise LLM inference scheme by dynamically adjusting processing batch, which can achieve near-zero idle computations without incurring additional resource consumption. To do so, BATON 1) shapes the vectors involved in the inference of the newly inserted query and processing batch to align dimensions and generates a new attention mask based on vector shaping to ensure inference correctness, which enables query inserting without consuming additional resource; 2) embeds prefilled Keys and Values of the new query into the KV_Cache of the processing batch by leveraging the prefilling and decoding separation mechanism, eliminating idle computations to the batch introduced by the prefilling process of the new query. Experimental results show that compared to the state-of-the-art solution Orca, BATON outperforms improves query processing by up to 1.75x.

This paper introduces a novel framework, M4, designed to estimate per-flow quantiles in data streams accurately. M4 is a versatile framework that can be integrated with a wide array of single-flow quantile estimation algorithms, thereby enabling them to perform per-flow estimation. The framework employs a sketch-based approach to provide a space-efficient method for recording and extracting distribution information. M4 incorporates two techniques:MINIMUMandSUM. TheMINIMUMtechnique minimizes the noise on a flow from other flows caused by hash collisions, while theSUMtechnique efficiently categorizes flows based on their sizes and customizes treatment strategies accordingly. We demonstrate the application of M4 on three single-flow quantile estimation algorithms (DDSketch,$t$-digest, and ReqSketch), detailing the specific implementation of theMINIMUMandSUMtechniques. We provide theoretical proof that M4 delivers high accuracy while utilizing limited memory. Additionally, we conduct extensive experiments to evaluate the performance of M4 regarding accuracy and speed. The experimental results indicate that across all three example algorithms, M4 significantly outperforms two comparison frameworks in terms of accuracy for per-flow quantile estimation while maintaining comparable speed.

Frequent object mining has gained considerable interest in the research community and can be split into frequent item mining and frequent set mining depending on the type of object. While existing sketch-based algorithms have made significant progress in addressing these two tasks concurrently, they also possess notable limitations. They either support only software platforms with low throughput or compromise accuracy for faster processing speed and better hardware compatibility. In this paper, we make a substantial stride towards supporting frequent object mining by designing SandwichSketch, which draws inspiration from sandwich making and proposes two techniques including the double fidelity enhancement and hierarchical hot locking to guarantee high fidelity on both two tasks. We implement SandwichSketch on three platforms (CPU, Redis, and FPGA) and show that it enhances accuracy by$38.4\times$and$5\times$for two tasks on three real-world datasets, respectively. Additionally, it supports a distributed measurement scenario with less than a 0.01% decrease in Average Relative Error (ARE) when the number of nodes increases from 1 to 16.

Finding top-$K$frequent items has been a hot topic in data stream processing with wide-ranging applications. However, most existing sketch algorithms focus on finding local top-$K$in a single data stream. In this paper, we tackle finding global top-$K$across multiple data streams. We find that using prior sketch algorithms directly is often unfair in global scenarios, degrading global top-$K$accuracy. We define top-$K$-fairness and show its importance for finding global top-$K$. To achieve this, we propose the Double-Anonymous (DA) sketch, where double-anonymity ensures fairness. We also propose two techniques, hot-filtering and early-freezing, to improve accuracy further. We theoretically prove that the DA sketch achieves top-$K$-fairness while maintaining high accuracy. Extensive experiments verify top-$K$-fairness in disjoint data streams, showing that the DA sketch's error is up to 129 times (60 times on average) smaller than the state-of-the-art. To enhance the applicability and technical depth, we also investigate how to extend the DA sketch to general distributed data stream scenarios and how to provide a fairer and more accurate global ranking for top-$K$items. The experimental results show that the extended version of the DA sketch can indeed compute better rankings and still has significant advantages in general data streams.

Approximate queries offer an efficient means of analyzing massive data streams under acceptable errors. Among these, subset queries over multiple attributes are common in many real-world applications. While sketches offer promising approximate solutions for massive data streams, efficiently supporting subset queries over multiple statistical attributes remains a significant challenge. To address this, we propose Hyper-USS, a novel sketching solution that accurately and efficiently supports subset queries over data streams involving multiple statistical attributes. With Joint Variance Optimization, Hyper-USS provides unbiased estimation and optimizes estimation variance jointly, addressing the challenge of accurately estimating multiple statistical attributes in the sketch design. The algorithm records the information of keys and all attributes in one sketch, ensuring high insertion efficiency. Furthermore, its three speed-optimized versions are introduced to handle the growing number of statistical attributes in data streams. Experimental results show that Hyper-USS and its three speed-optimized versions consistently surpass state-of-the-art methods that support subset queries in both estimation accuracy and insertion throughput. Specifically, Hyper-USS improves accuracy by at least 38%, while the algorithm and its three speed-optimized versions achieve throughput improvements of up to$31.90\times$,$45.31\times$,$49.21\times$, and$58.03\times$, respectively.

The growing memory demands of embedding tables in Deep Learning Recommendation Models (DLRMs) pose great challenges for model training and deployment. Existing embedding compression solutions cannot simultaneously achieve memory efficiency, low latency, and adaptability to dynamic data distribution. This article presents CAFE+, a Compact, Adaptive, and Fast Embedding compression framework that meets the above requirements. The design philosophy of CAFE+ is to dynamically allocate more memory to important features and less to unimportant ones. We assign unique embedding to important feature and allow multiple unimportant features sharing one embedding. We propose a fast and lightweight feature monitor, to real-time capture feature importance and report important features. We theoretically analyze the accuracy of our feature monitor and prove the superiority of CAFE+ from the aspect of model convergence. Extensive experiments show CAFE+ outperforms existing embedding compression methods, yielding \(3.94\%\) and \(3.94\%\) superior testing AUC on Criteo Kaggle dataset and CriteoTB dataset at a compression ratio of \(10{,}000\times\) . Building on our conference version [ 114 ], this journal version introduces several novel designs (implicit importance attenuation, adaptive threshold adjustment, and ColdSifter) that enable CAFE+ to more effectively adapt to long-term online learning and achieve better model quality. All codes are available at GitHub [ 112 ].

Sketch algorithms are crucial for identifying top-k items in large-scale data streams. Existing methods often compromise between performance and accuracy, unable to efficiently handle increasing data volumes with limited memory. We present Bubble Sketch, a compact algorithm that excels in both performance and accuracy. Bubble Sketch achieves this by (1) Recording only full keys of hot items, significantly reducing memory usage, and (2) Using threshold relocation to resolve conflicts, enhancing detection accuracy. Unlike traditional methods, Bubble Sketch eliminates the need for a Min-Heap, ensuring fast processing speeds. Experiments show Bubble Sketch outperforms the other seven algorithms compared, with the highest throughput and precision, and surpasses HeavyKeeper in accuracy by up to two orders of magnitude.

In key-value storage scenarios where storage space is at a premium, our focus is on a class of solutions that only store the value, which is highly space-efficient. While these solutions have proven their worth in distributed storage, networking, and bioinformatics, they still face two significant issues: one is that their space cost could be further reduced; the other is their are vulnerable to update failures, which can necessitate a complete table reconstruction. To address these issues, we introduce VisionEmbedder, a compact key-value embedder with constant-time lookup, fast dynamic updates, and a near-zero risk of reconstruction. VisionEmbedder cuts down the storage requirement from 2.2L bits to just 1.6L bits per key-value pair with an L-bit value, and it significantly reduces the chance of update failures by a factor of n, where$n$is the number of keys (for instance, 1 million or more). The compromise with VisionEmbedder comes with a minor reduction in query throughput on certain data sizes. The enhancements offered by VisionEmbedder have been theoretically validated and are effective across any dataset. Additionally, we have implemented VisionEmbedder on both FPGA and CPU platforms, with all codes made available as open-source.

In quantile estimation within a stream of key-value pairs, recent work has made significant progress in query flexibility, supporting quantile estimation for any key using a unified statistical structure. However, despite this flexibility, their query speed falls behind, unable to match the high speed of online data insertion. This “offline query + online insertion” model is not ideal for online quantile estimation. Our goal is to online detect keys whose quantiles exceed a user-queried threshold in real-time, such as identifying the user whose 95 % latency exceeds 200ms in network data. These keys, termed “Quantile-Outstanding Keys,” are vital for anomaly detection in streaming data. In this paper, we propose QuantileFilter, the first approximate algorithm specifically designed for detecting quantile-outstanding keys. QuantileFilter overcomes existing limitations by 1) enabling fast online computation, capable of handling streaming data in real-time with a constant processing time for each data item, accelerating the state-of-the-art (SOTA) by 10 ~ 100 times, and 2) maintaining high space efficiency, saving 50 ~ 500 times storage space compared to the SOTA while maintaining the same accuracy. All associated code is available on GitHub.

Sketch is a probabilistic data structure widely used in various fields due to its high accuracy under small memory. Designing hierarchical data structures for real-world datasets with high skewness is one of the main optimization directions of Sketch. However, there is still a big accuracy gap between the existing sketches and the optimum. To fill the gap, we propose a new sketch called Coding Sketch. For the first time, we used both hierarchical structure and nearly-lossless encoding-and-decoding to compress frequent items, which significantly improves the accuracy of frequent items. Besides, we propose flagless pruning to remove the additional flag bits in traditional hierarchical structure. Thus Coding Sketch can optimize the frequency estimation of both frequent and infrequent items. Our evaluation shows that our algorithm is 10 times more accurate than the state-of-the-art under the same memory cost. All related codes are open-sourced.22https://github.com/CodingSketch/Coding-Sketc

Dynamic graphs are gaining importance in many real-world applications based on different graph queries. Due to the large volume and high dynamicity, people resort to compute approximations to answer graph queries. However, previous work primarily evaluates the relationship between nodes based on frequency, which is not sufficient in many cases. We observe that this relationship varying process is highly similar to the water cooling process in nature. Based on the observation, we formulate a new concept Intimacy with Newton's law of cooling, to illustrate the relationship between nodes. Currently, there is no prior algorithm tailored for Intimacy estimation. Because Intimacy varies in every time unit, the main challenge lies in how to record and update the Intimacy efficiently. In this paper, we propose a novel technique named Newton-Observe to address this challenge. The key idea of Newton-Observe is that we only decay the Intimacy when we observe/query it. Based on Newton-Observe, we develop a series of Newton sketches to answer three fundamental tasks of Intimacy in dynamic graphs. We theoretically prove that the Newton sketch can estimate the Intimacy within an additive constant error to the real Intimacy. Our experiments on real-world datasets and synthetic datasets show that Newton-Observe outperform the strawman solution by up to$570\times$smaller ARE and improve the throughput by up to$1.62\times$. All source codes are open sourced at Github anonymously.

The field of quantile estimation has grown in importance due to its myriad practical applications. Recent research trends have evolved from estimating the quantile for a single data stream to developing data structures that can concurrently estimate quantiles for multiple sub-streams, also known as flows. This paper introduces a novel framework, M4, designed to estimate per-flow quantiles in data streams accurately. M4 is a versatile framework that can be integrated with a wide array of single-flow quantile estimation algorithms, thereby enabling them to perform per-flow estimation. The framework employs a sketch-based approach to provide a space-efficient method for recording and extracting distribution information. M4 incorporates two techniques: MINIMUM and SUM. The MINIMUM technique minimizes the noise on a flow from other flows caused by hash collisions, while the SUM technique efficiently categorizes flows based on their sizes and customizes treatment strategies accordingly. We demonstrate the application of M4 on three single-flow quantile estimation algorithms (DDSketch, t-digest, and ReqSketch), detailing the specific implementation of the MINIMUM and SUM techniques. We provide theoretical proof that M4 delivers high accuracy while utilizing limited memory. Additionally, we conduct extensive experiments to evaluate the performance of M4 regarding accuracy and speed. The experimental results indicate that across all three example algorithms, M4 significantly outperforms two comparison frameworks in terms of accuracy for per-flow quantile estimation while maintaining comparable speed.

Sketch has been widely used in the field of large-scale data stream processing. However, common fixed-counter algorithms such as Count-Min Sketch have to allocate larger counters, which wastes a lot of memory due to the high skewness of real-world data streams. To reduce memory usage, we propose to dynamically adjust the counter size that matches the distribution of the data stream. We introduce BitMatcher, a fast global-adjusting algorithm that automatically adjusts the counter to the appropriate size to match the data stream. During stream processing, BitMatcher identifies items hashed into a bucket based on isolated fingerprints. If it overflows, BitMatcher changes the flag bits in the bucket and dynamically increases or shrinks the size of some counters in a fine-grained manner. BitMatcher can also relocate a cold item in the bucket with the idea of cuckoo hashing to preserve the potential hot item while achieving global load balancing. Through the above way of dealing with overflow caused by skewed data, BitMatcher precisely manipulates allocated bits and maximizes memory utilization. The experiments show that BitMatcher has high throughput and can outperform SOTA by up to 4 orders of magnitude in terms of accuracy. We also deployed BitMatcher on several platforms, showing its software and hardware scalability.

In data stream mining, monitoring high-speed users and segregating their excessive use, known as “Overspeed items,” is crucial for preventing system overload and maintaining fairness in messaging and network systems. Current approaches, however, face scalability challenges with large user bases, primarily due to increasing memory requirements proportional to user numbers. We have pinpointed the inefficiency in allocating memory for all users, recognizing that only a small fraction exhibit overspeed behavior at any given time. Addressing this, we employed the sketching technique, a type of approximate algorithm, and designed the first sketch algorithm for finding Overspeed items, named SpeedSketch: (1) Scalability. SpeedSketch can scale user numbers (saving memory space) to a factor of 6430 while maintaining a low average error rate of 0.1% in real-world datasets. (2) Accuracy. In theory, SpeedSketch stands out as the only sketch algorithm offering a per-user relative error bound. (3) Speed. SpeedSketch is implemented on a high-speed programmable switch with a throughput capacity of 4.8 billion items per second. All codes are available on GitHub for reference.

Recently, the growing memory demands of embedding tables in Deep Learning Recommendation Models (DLRMs) pose great challenges for model training and deployment. Existing embedding compression solutions cannot simultaneously meet three key design requirements: memory efficiency, low latency, and adaptability to dynamic data distribution. This paper presents CAFE, a Compact, Adaptive, and Fast Embedding compression framework that addresses the above requirements. The design philosophy of CAFE is to dynamically allocate more memory resources to important features (called hot features), and allocate less memory to unimportant ones. In CAFE, we propose a fast and lightweight sketch data structure, named HotSketch, to capture feature importance and report hot features in real time. For each reported hot feature, we assign it a unique embedding. For the non-hot features, we allow multiple features to share one embedding by using hash embedding technique. Guided by our design philosophy, we further propose a multi-level hash embedding framework to optimize the embedding tables of non-hot features. We theoretically analyze the accuracy of HotSketch, and analyze the model convergence against deviation. Extensive experiments show that CAFE significantly outperforms existing embedding compression methods, yielding 3.92% and 3.68% superior testing AUC on Criteo Kaggle dataset and CriteoTB dataset at a compression ratio of 10000x. The source codes of CAFE are available at GitHub.

Batch is an important pattern in data streams, which refers to a group of identical items that arrive closely. We find that some special batches that arrive periodically are of great value. In this paper, we formally define a new pattern, namely periodic batches. A group of periodic batches refers to several batches of the same item, where these batches arrive periodically. Studying periodic batches is important in many applications, such as caches, financial markets, online advertisements, networks, etc. This paper proposes a unified framework, namely the HyperCalm sketch, to detect batch and periodic batch in data streams. HyperCalm sketch takes two phases to detect periodic batches. In phase 1, we propose a time-aware Bloom filter, called HyperBloomFilter (HyperBF), to detect batches. In phase 2, we propose an enhanced top-k algorithm, called Calm Space-Saving (CalmSS), to report top-itk periodic batches. Extensive experiments show HyperCalm outperforms the strawman solutions 4× in term of average relative error and 98.1× in term of speed. All related codes are open-sourced.

In global data analysis, the central server needs the global statistic of the user data stored in local clients. In such cases, an Honest-but-Curious central server might put user privacy at risk in trying to collect individual statistics of each user. In response, the secure aggregation provides a solution for calculating global statistics without revealing users’ privacy data. However, existing secure aggregation protocols only focus on the data in the form of vectors or common sets, which limits their application scope. We formalize a general problem—key-value set secure aggregation—that not only includes secure vector aggregation and private set union but also supports more applications. To address the proposed problem, we devise our solution (called the KVSAgg framework) that promises satisfactory performance in security, efficiency, and accuracy. Our key technique is a homomorphic transform algorithm (called HyperIBLT) that is not only capable of bidirectionally transforming data between key-value sets and vectors, but also able to transform sum operation of sets to addition of vectors. We implement KVSAgg on both CPU and GPU platforms and perform the evaluation on three use cases including federated learning, distributed data counting, and finding global hot items. Compared with our baselines, KVSAgg simultaneously achieves the best security, efficiency higher by orders of magnitude, and zero-error in nearly all cases. All codes are open-source anonymously.

In this paper, we propose a new type of item in data streams, called simplex items. Simplex items have frequencies in consecutive p windows that can be approximated by a polynomial of degree at most k, where k = 0, 1, 2. These low-order representable simplex items have a wide range of potential applications. For example, when k = 1, we can leverage these items whose frequency has obvious linear increase or decrease to speed up the running time of a class of machine learning models and detect network attacks such as distributed denial-of-service (DDoS), etc. To find k-degree simplex items in real time, we propose a novel sketch, namely X-Sketch, to accurately record simplex items in a compact space. The key idea of X-Sketch is to effectively filter out non-simplex items with less memory overhead, and then monitor the remaining potential simplex items and keep those items with more consecutive windows. We conduct extensive experiments, and the experimental results show that the F1 Score of X-Sketch is on average 68.6%, 57.9%, and 42.2% higher than the baseline solution for k = 0, 1, 2, respectively. Finally, we also provide a case study that applies X-Sketch to "accelerate" the two machine learning models through end-to-end experiments. We have released our source code at GitHub.

Batch is an important pattern in data streams, which refers to a group of identical items that arrive closely. We find that some special batches that arrive periodically are of great value. In this paper, we formally define a new pattern, namely periodic batches. A group of periodic batches refers to several batches of the same item, where these batches arrive periodically. Studying periodic batches is important in many applications, such as caches, financial markets, online advertisements, networks, etc. We propose a one-pass sketching algorithm, namely the HyperCalm sketch, which takes two phases to detect periodic batches in real time. In phase 1, we propose a time-aware Bloom filter, namely HyperBloomFilter (HyperBF), to detect the start of batches. In phase 2, we propose an enhanced top-k algorithm, called Calm Space-Saving (CalmSS), to report top-k periodic batches. We theoretically derive the error bounds for HyperBF and CalmSS. Extensive experiments show HyperCalm outperforms the strawman solutions 4× in term of average relative error and 13.2× in term of speed. We also apply HyperCalm to a cache system and integrate HyperCalm into Apache Flink. All related codes are open-sourced.

Sketches have risen as promising solutions for frequency estimation, which is one of the most fundamental tasks in approximate data stream processing. In many scenarios, users have a strong demand to apply sketches under the expected error constraints. In this paper, we explore how to configure sketch parameters to satisfy user-defined error constraints. We propose SketchConf, an automatic sketch configuration framework, which efficiently generates memory-optimal configurations for the first time. We show that SketchConf can be applied to order-independent sketches, including CM, Count, Tower, and Nitro sketches. We further discuss how to deal with the unknown and changeable workloads when applying SketchConf to the real scenarios of streaming data processing. Experimental results show that SketchConf can be up to 715.51 times faster than the baseline algorithm, and the outputted configurations save up to 99.99% memory and achieve up to 27.44 times throughput, compared with the theory-based configurations. The code is open sourced at Github.

Graphs are good at presenting relational and structural information, making it powerful in the representation of various data. For the efficient storage and processing of graph-like data, graph databases have been rapidly developed and extensively studied. However, graph databases mostly use adjacency lists as their basic data structure (e.g., Neo4j), which could result in poor performance of edge due to the skewed degree distribution of graphs.We design the Wind-Bell Index to address this problem. Wind-Bell Index is a memory-efficient index data structure, which can be attached to existing graph databases to speed up the edge. We have fully implemented our data structure in Neo4j, the most popular graph database today, and conduct theoretical and experimental analysis to evaluate the performance. Theoretical results prove the high query efficiency of our algorithm. And experimental results show that the average edge query speed is increased by hundreds of times compared with the original query interface of Neo4j. We believe that the excellent performance and scalability of Wind-Bell Index make it suitable for the application in a variety of graph databases.

A range filter is a data structure to answer range membership queries. Range queries are common in modern applications, and range filters have gained rising attention for improving the performance of range queries by ruling out empty range queries. However, state-of-the-art range filters, such as SuRF and Rosetta, suffer either high false positive rate or low throughput. In this paper, we propose a novel range filter, called REncoder. It organizes all prefixes of keys into a segment tree, and locally encodes the segment tree into a Bloom filter to accelerate queries. REncoder supports diverse workloads by adaptively choosing how many levels of the segment tree to store. We theoretically prove that the error of REncoder is bounded and derive the asymptotic space complexity under the bounded error. We conduct extensive experiments on both synthetic datasets and real datasets. The experimental results show that REncoder outperforms all state-of-the-art range filters.

High-accuracy real-time data stream estimations are critical for various applications, and sliding-window-based techniques have attracted wide attention. However, existing solutions struggle to achieve high accuracy, generality, and low memory usage simultaneously. To overcome these limitations, we present MicroscopeSketch, a high-accuracy sketch framework. Our key technique, called adaptive zooming, dynamically adjusts the granularity of counters to maximize accuracy while minimizing memory usage. By applying MicroscopeSketch to three specific tasks---frequency estimation, top-k frequent items discovery, and top-k heavy changes identification-we demonstrate substantial improvements over existing methods, reducing errors by roughly 4 times for frequency estimation and 3 times for identifying top-k items. The relevant source code is available in a GitHub repository.

1Estimating the quantile of distribution, especially tail distribution, is an interesting topic in data stream models, and has obtained extensive interest from many researchers. In this paper, we propose a novel sketch, namely SketchPolymer to accurately estimate per-item tail quantile. SketchPolymer uses a technique called Early Filtration to filter infrequent items, and another technique called VSS to reduce error. Our experimental results show that the accuracy of SketchPolymer is on average 32.67 times better than state-of-the-art techniques. We also implement our SketchPolymer on P4 and FPGA platforms to verify its deployment flexibility. All our codes are available at GitHub.[1]

Sketching algorithms are considered as promising solutions for answering approximate query on massive data stream. In real scenarios, a large number of problems can be abstracted as subset query over multiple attributes. Existing sketches are designed for query on single attributes, and therefore are inefficient for query on multiple attributes. In this work, we propose Hyper-USS, an innovative sketching algorithm that supports subset query over multiple attributes accurately and efficiently. To the best of our knowledge, this work is the first sketching algorithm designed to answer approximate query over multi-attribute data stream. We utilize the key technique, Joint Variance Optimization, to guarantee high estimation accuracy on all attributes. Experiment results show that, compared with the state-of-the-art (SOTA) sketches that support subset query on single attributes, Hyper-USS improves the accuracy by 16.67X and the throughput by 8.54X. The code is open-sourced at Github.

We abstract a MIMO scenario in distributed data stream mining, where a stream of multiple items is mined by multiple nodes. We design a framework named MimoSketch for the MIMO-specific scenario, which improves the fundamental mining task of item frequency estimation. MimoSketch consists of an algorithm design and a policy to schedule items to nodes. MimoSketch's algorithm applies random counting to preserve a mathematically proven unbiasedness property, which makes it friendly to the aggregate query on multiple nodes; its memory layout is dynamically adaptive to the runtime item size distribution, which maximizes the estimation accuracy by storing more items. MimoSketch's scheduling policy balances items among nodes, avoiding nodes being overloaded or underloaded, which improves the overall mining accuracy. Our prototype and evaluation show that our algorithm can improve the item frequency estimation accuracy by an order of magnitude compared with the state-of-the-art solutions, and the scheduling policy further promotes the performance in MIMO scenarios.

Membership (membership query/membership testing) is a fundamental problem across databases, networks and security. However, previous research has primarily focused on either approximate solutions, such as Bloom Filters, or exact methods, like perfect hashing and dictionaries, without attempting to develop an integral theory. In this paper, we propose a unified and complete theory, namely chain rule, for general membership problems, which encompasses both approximate and exact membership as extreme cases. Building upon the chain rule, we introduce a straightforward yet versatile algorithm framework, namely ChainedFilter, to combine different elementary filters without losing information. Our evaluation results demonstrate that ChainedFilter improves performance of many applications including static dictionary, lossless data compression, Cuckoo Hashing, LSM-Tree and Learned Filters.

Data stream processing is critical in streaming databases. Existing works pay a lot of attention to frequent items. To improve the accuracy for frequent items, existing solutions focus on accurately filtering infrequent items. While these solutions are effective, they keep track of all infrequent items and require multiple hash computations and memory accesses. This increases memory and time overhead. To reduce this overhead, we propose LadderFilter, which candiscard infrequent items efficiently in terms of both memory and time. To achieve memory efficiency, LadderFilter discards (approximately) infrequent items using multiple LRU queues. To achieve time efficiency, we leverage SIMD instructions to implement LRU policy without timestamps. We apply LadderFilter to four types of sketches. Our experimental results show that LadderFilter improves the accuracy by up to 60.6×, and the throughput by up to 1.37×, and can maintain high accuracy with small memory usage. All related code is provided open-source at Github.

A Sketch is an excellent probabilistic data structure, which records the approximate statistics of data streams. Linear additivity is an important property of sketches. This paper studies how to keep the linear property after sketch compression. Most existing compression methods do not keep the linear property. We propose TreeSensing, an accurate, efficient, and flexible framework to linearly compress sketches. In TreeSensing, we first separate a sketch into two parts according to counter values. For the sketch with small counters, we propose a technique called TreeEncoding to compress it into a hierarchical structure. For the sketch with large counters, we propose a technique called SketchSensing to compress it using compressive sensing. We theoretically analyze the accuracy of TreeSensing. We use TreeSensing to compress 7 sketches and conduct two end-to-end experiments: distributed measurement and distributed machine learning. Experimental results show that TreeSensing outperforms prior art on both accuracy and efficiency, which achieves up to 100× smaller error and 5.1× higher speed than state-of-the-art Cluster-Reduce. All related codes are open-sourced.

Inner-product estimation is the base of many important tasks in a variety of big data scenarios, including measuring similarity of streams in data stream processing, estimating join size in database, and analyzing cosine similarity in various applications. Sketch, as a class of probability algorithms, is promising in inner-product estimation. However, existing sketch solutions suffer from low accuracy due to their neglect of the high skewness of real data. In this paper, we design a new sketch algorithm for accurate and unbiased inner-product estimation, namely JoinSketch. To improve accuracy, JoinSketch consists of multiple components, and records items with different frequency in different components. We theoretically prove that JoinSketch is unbiased, and has lower variance compared with the well-known AGMS and Fast-AGMS sketch. The experimental results show that JoinSketch improves the accuracy by 10 times in average while maintaining a comparable speed. All code is open-sourced at Github.

Finding top-K frequent items has been a hot topic in data stream processing in recent years, which has a wide range of applications. However, most of existing sketch algorithms focuses on finding local top-K in a single data stream. In this paper, we work on finding global top-K in multiple disjoint data streams. We find that directly deploying prior sketch algorithms is often unfair under global scenarios, which will degrade the accuracy of global top-K. We define top-K-fairness and show that it is important for finding global top-K. To achieve top-K-fairness, we propose a new sketch framework, called the Double-Anonymous sketch. The process of finding global top-K items is similar to that of paper reviewing and democratic elections. In these scenarios, double-anonymity is often an effective strategy to achieve top-K-fairness. We also propose two techniques, hot panning, and early freezing, to further improve the accuracy. We theoretically prove that the Double-Anonymous sketch achieves top-K-fairnesswhile keeping high accuracy. We perform extensive experiments to verify top-K-fairness in the scenario of disjoint data streams. The experimental results show that the Double-Anonymous sketch's error is up to 129 times (60 times on average) smaller than the state-of-the-art. All the related source code is open-sourced and available at Github.

Recent works explore several attacks against Machine-Learning-as-a-Service (MLaaS) platforms (e.g., the model stealing attack), allegedly posing potential real-world threats beyond viability in laboratories. However, hampered by model-type-sensitive , most of the attacks can hardly break mainstream real-world MLaaS platforms. That is, many MLaaS attacks are designed against only one certain type of model, such as tree models or neural networks. As the black-box MLaaS interface hides model type info, the attacker cannot choose a proper attack method with confidence, limiting the attack performance. In this paper, we demonstrate a system, named Sniffer, that is capable of making model-type-sensitive attacks "great again" in real-world applications. Specifically, Sniffer consists of four components: Generator, Querier, Probe, and Arsenal. The first two components work for preparing attack samples. Probe, as the most characteristic component in Sniffer, implements a series of self-designed algorithms to determine the type of models hidden behind the black-box MLaaS interfaces. With model type info unraveled, an optimum method can be selected from Arsenal (containing multiple attack methods) to accomplish its attack. Our demonstration shows how the audience can interact with Sniffer in a web-based interface against five mainstream MLaaS platforms.

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

In this paper, we propose a generic sketch algorithm capable of achieving more accuracy in the following five tasks: finding top-$k$frequent items, finding heavy hitters, per-item frequency estimation, and heavy changes in the time and spatial dimension. The state-of-the-art (SOTA) sketch solution for multiple measurement tasks is ElasticSketch (ES). However, the accuracy of its frequency estimation has room for improvement. The reason for this is that ES suffers from overestimation errors in the light part, which introduces errors when querying both frequent and infrequent items. To address these problems, we propose a generic sketch, OneSketch, designed to minimize overestimation errors. To achieve the design goal, we propose four key techniques, which embrace hash collisions and minimize possible errors by handling highly recurrent item replacements well. Experimental results show that OneSketch clearly outperforms 12 SOTA schemes. For example, compared with ES, OneSketch achieves more than 10× lower Average Absolute Error on finding top-$k$frequent items and heavy hitters, as well as 48.3% and 38.4% higher F1 Scores on two heavy changes under 200 KB memory, respectively.

The fundamental issue of how to calculate the false positive probability of widely used Bloom Filters (BF), from which the conventional wisdom is to derive the optimal value of$k$, remains elusive. Since Bloom gave the false positive formula in 1970, in 2008, Boseet al. pointed out that Bloomˆs formula is flawed; and in 2010, Christensenet al. pointed out that Bose's formula is also flawed and gave another formula. Although Christensen's formula is perfectly accurate, it is time-consuming and impossible to calculate the optimal value of$k$. Based on the following observation: for a BF with$m$bits and$n$elements, if and only if its entropy is the largest, its false positive probability is the smallest, we propose the first approach to calculating the optimal$k$without any false positive formula. Furthermore, we propose a new and more accurate upper bound for the false positive probability. When the size of a Bloom Filter becomes infinitely large, our upper bound turns equal to the lower bound, which becomes Bloomˆs formula and deepens our understanding towards it. Besides, we derive the bounds of correct rate of Counting Bloom Filters (CBFs) by applying our proposed formulas about BFs to them.

Nowadays, research on temporal membership queries is indispensable. Generally, temporal membership queries exist in two modalities: fixed windows and sliding windows, the latter having obvious advantages. The first sketch that implements temporal membership queries is the persistent Bloom filter (PBF). PBF has two shortcomings: it does not support sliding windows nor frequency queries. Here, we propose HoppingSketch to promote the original PBF. It is the first sketch that implements temporal membership queries for sliding windows. HoppingSketch is a general and efficient data stream processing framework, able to implement different tasks thanks to different atomic sketches. When the atomic sketches are Bloom filters and we apply them to PBF, HoppingSketch can achieve significantly higher temporal membership query accuracy than the original PBF. When the atomic sketches are sketches of Count-Min, Conservative Update, and Count, HoppingSketch can achieve more accurate frequency query than by applying PBF on the corresponding sketches. Our experimental results demonstrate the advantages of HoppingSketch compared with the state-of-the-art.

Data stream processing has become a hot issue in recent years due to the arrival of big data era. There are three fundamental stream processing tasks: membership query, frequency query and Top-K query. While most existing solutions address these queries in fixed windows, this paper focuses on a more challenging task: answering these queries in sliding windows. While most existing solutions address different kinds of queries by using different algorithms, this paper focuses on a generic framework. In this paper, we propose a generic framework, namely Sliding sketches, which can be applied to many existing solutions for the above three queries, and enable them to support queries in sliding windows. We apply our framework to five state-of-the-art sketches for the above three kinds of queries. Theoretical analysis and extensive experimental results show that after using our framework, the accuracy of existing sketches that do not support sliding windows becomes much higher than the corresponding best prior art. We released all the source code at Github.

A graph stream is a continuous sequence of data items, in which each item indicates an edge, including its two endpoints and edge weight. It forms a dynamic graph that changes with every item. Graph streams play important roles in cyber security, social networks, cloud troubleshooting systems and more. Due to the vast volume and high update speed of graph streams, traditional data structures for graph storage such as the adjacency matrix and the adjacency list are no longer sufficient. However, prior art of graph stream summarization either supports limited kinds of queries or suffers from poor accuracy of query results. In this paper, we propose a novelGraphStreamSketch (GSS for short) to summarize the graph streams, which has linear space cost$O(|E|)$(E is the edge set of the graph) and high update speed, and supports most kinds of queries over graph streams with controllable errors. Experimental results show that our solution is up to 142 times faster than the adjacency list when processing updates in graph streams, and its memory consumption is as small as$30\%$of the adjacency list. Though error is introduced as a trade off in our solution, both theoretical analysis and experiment results confirm that such error is small and controllable. The relative error is below$10^{-2}$in edge weight query, and the precision is above$90\%$is 1-hop precursor/successor queries.

Bloom filter is an efficient data structure for filtering negative keys (keys not in a given set) with substantially small space. However, in real-world applications, there widely exist vulnerable negative keys, which will bring high costs if not being properly filtered, especially when positive keys are added/deleted dynamically. Such problem gets more severe when keys within one set are dynamically added or deleted. Recently, there are works focusing on handling such (vulnerable) negative keys by incorporating learning techniques. These learning-based filters fail to work as the learning techniques can hardly handle incremental insertions or deletions. To address the problem, we proposeSeeSawCountingFilter (SSCF), which is innovated with encapsulating the vulnerable negative keys into a unified counter array named seesaw counter array, and dynamically modulating (or varying) the applied hash functions to guard the encapsulated keys from being misidentified. Moreover, we design ada-SSCF to handle the scenarios where the vulnerable negative keys cannot be obtained in advance. We extensively evaluate our SSCF, which shows that SSCF outperforms the cutting-edge filters by$3\times$on averages regarding accuracy while ensuring a low operation latency. All source codes are in (SSCF-authors).

Burstis a common pattern in data streams which is characterized by a sudden increase in terms of arrival rate followed by a sudden decrease. Burst detection has attracted extensive attention from the research community. To detect bursts accurately in real time, we propose a novel sketch, namely BurstSketch, which consists of two stages. Stage 1 uses the technique Running Track to select potential burst items efficiently. Stage 2 monitors the potential burst items and captures the key features of burst pattern by a technique called Snapshotting. We further propose an optimization, namely Dynamic Buckets, which can improve the accuracy of BurstSketch. We provide theoretical error bounds for Stage 1, Stage 2 and the optimized version. Experimental results show that, compared with the strawman solution, Burstsketch achieves 2.00 to 11.63 times higher F1 score, and 1.56 times higher throughput. We also integrate BurstSketch into Apache Flink, and show that using BurstSketch can be faster than simply using the built-in APIs provided by Apache Flink.

In this paper, we study periodic items in data streams, which refer to those items arriving with a fixed interval. All existing works involving mining periodic patterns does not fit for data stream scenarios. To find periodic items in real time, we propose a novel sketch, PeriodicSketch, aiming to accurately record top-$K$periodic items. To the best of our knowledge, this is the first work to find periodic items in data streams. Any interval may occur many times, and we use frequency to denote the number of an interval occurred. To pick out periodic items with high frequency, we propose a key technique called Guaranteed Soft Uniform (GSU) replacement strategy. Our theoretical proofs show that when replacement is successful, it is more likely that the new item has a higher frequency than the current smallest frequency; and GSU can ensure that our items in the sketch will approach the true periodic items closer and closer. And as soon as we get all the periodic items, the state would not change worse with high probability. We conduct extensive experiments, and the experimental results show that the Average Absolute Error (AAE) of our sketch using 1/10 memory is around 737 times (up to 2019 times) lower than the baseline solution. Finally, we provide a concrete case: Cache prefetch, which proves that PeriodicSketch can significantly improve the Cache hit ratio. All related codes of PeriodicSketch are open-sourced and available at GitHub [1].

Data stream processing has become fundamental in computer science, with a wide range of applications, such as in databases, data mining, and security. Memorizing when an item appears in the data stream is one important task in stream processing. Because the older data is, the less value it has, memorizing recent events with higher accuracy is desirable. To achieve this, we propose a novel data stream processing structure named the Stair sketch. Our key idea is to organize the memory used by different time periods in the shape of stairs. We deploy the Stair sketch on Bloom filters, CM sketches, and CU sketches as case studies. Experiment results show that our approach outperforms state-of-the-art algorithms by more than 5× in accuracy while providing comparable efficiency. The source code of the Stair sketch is available at GitHub.

Nowadays, wide-area data analyses are pervasive with emerging geo-distributed systems. These analyses often need to do the global aggregation in the wide area. Since scarce and variable WAN bandwidth may degrade the aggregation performance, it is highly desired to design a communication scheme for global aggregation in WAN. Unfortunately, no existing algorithm can meet the three design requirements of communication schemes: fast computation, adaptive transmission, and accurate aggregation. In this paper, we propose MinMax Sampling, a fast, adaptive, and accurate communication scheme for global aggregation in WAN. We first focus on the accuracy and design a scheme, namely MinMaxopt, to achieve optimal accuracy. However, MinMaxopt does not meet the other two requirements: fast computation and adaptive transmission. Based on MinMaxopt, we propose MinMaxadp, which trades little accuracy for the other two requirements. We evaluate MinMaxadp with three applications: federated learning, distributed state aggregation, and hierarchical aggregation. Our experimental results show that MinMaxadp is superior to existing algorithms (8.44× better accuracy on average) in all three applications. The source codes of MinMax Sampling are available at Github [1].

Bloom filter is an efficient data structure for filtering negative keys (keys not in a given set) with substantially small space. However, in real-world applications, there widely exist vulnerable negative keys, which will bring high costs if not being properly filtered, especially when positive keys are added/deleted dynamically. To address the problem, we propose SeeSaw Counting Filter (SSCF), which is innovated with encapsulating the vulnerable negative keys into a unified counter array named seesaw counter array, and dynamically modulating (or varying) the applied hash functions to guard the encapsulated keys from being misidentified. Moreover, we propose ada-SSCF to handle the scenarios where the vulnerable negative keys cannot be obtained in advance. We extensively evaluate our SSCF, which shows that SSCF outperforms the cutting-edge filters by 3 × on averages regarding accuracy while ensuring a low operation latency. All source codes are in [2].

Flow scheduling is crucial in data centers, as it directly influences user experience of applications. According to different assumptions and design goals, there are four typical flow scheduling problems/solutions: SRPT, LAS, Fair Queueing, and Deadline-Aware scheduling. When implementing these solutions in commodity switches with limited number of queues, they need to set static parameters by measuring traffic in advance, while optimal parameters vary across time and space. This paper proposes a generic framework, namely QCluster, to adapt all scheduling problems for limited number of queues. The key idea of QCluster is to cluster packets with similar weights/properties into the same queue. QCluster is implemented in Tofino switches, and can cluster packets at a speed of 3.2 Tbps. To the best of our knowledge, QCluster is the fastest clustering algorithm. Experimental results in testbed with programmable switches and ns-2 show that QCluster reduces the average flow completion time (FCT) for short flows up to 56.6%, and reduces the overall average FCT up to 21.7% over state-of-the-art. All the source code in ns-2 is available in Github [45].

Recording the frequency of items in highly skewed data streams is a fundamental and hot problem in recent years. The literature demonstrates that sketch is the most promising solution. The typical metrics to measure a sketch are accuracy and speed, but existing sketches make only trade-offs between the two dimensions. Our proposed solution is a new sketch framework called Stingy sketch with two key techniques: Bit-pinching Counter Tree ( BCTree ) and Prophet Queue ( PQueue ) which optimizes both the accuracy and speed. The key idea of BCTree is to split a large fixed-size counter into many small nodes of a tree structure, and to use a precise encoding to perform carry-in operations with low processing overhead. The key idea of PQueue is to use pipelined prefetch technique to make most memory accesses happen in L2 cache without losing precision. Importantly, the two techniques are cooperative so that Stingy sketch can improve accuracy and speed simultaneously. Extensive experimental results show that Stingy sketch is up to 50% more accurate than the SOTA of accuracy-oriented sketches and is up to 33% faster than the SOTA of speed-oriented sketches.

Finding top-$k$frequent items has been a hot issue in databases. Finding top-$k$persistent items is a new issue, and has attracted increasing attention in recent years. In practice, users often want to know which items are significant,i.e., not only frequent but also persistent. No prior art can address both of the above two issues at the same time. Also, for high-speed data streams, prior art cannot achieve high accuracy when the memory is tight. In this paper, we define a new issue, named finding significant items, and propose a novel algorithm namely LTC to address this issue. It includes two key techniques, Long-tail Restoring and CLOCK, as well as three optimizations. In addition, LTC is extended to support finding significant items with thresholds. We theoretically derive the correct rate and error bound, and conduct extensive experiments on three real datasets to test the performance of LTC. Our experimental results show that LTC can achieve$10^5$times higher accuracy in terms of average relative error than other related algorithms. Lastly, LTC is applied to a DDoS detection task and it shows that finding significant items is more powerful than finding frequent items.

Multi-set membership queries are fundamental operations in data science. In this paper, we propose a new data structure for multi-set membership queries, named coloring embedder, which is fast, accurate, and memory efficient. The idea of coloring embedder is to first map elements to a high-dimensional space, which nearly eliminates hashing collisions, and then use a dimensional reduction representation, similar to coloring a graph, to save memory. Theoretical proofs and experimental results show that the coloring embedder is effective in solving the problem of multi-set membership queries. We also find that web cache sharing is one of the typical application scenarios of the multi-set membership queries and current methods based on Bloom filters always send redundant queries. We apply coloring embedder to web cache sharing by arranging our data structure on the on-chip and off-chip memory and designing query, insertion and deletion operations for this scenario. The experimental results show that compared with the present method, our method can reduce the queries sent by proxies while reaching equal hit rate with the same size of on-chip memory. The source code of coloring embedder has been released on Github.

Perfect hashing is a hash function that maps a set of distinct keys to a set of continuous integers without collision. However,most existing perfect hash schemes are static, which means that they cannot support incremental updates, while most datasets in practice are dynamic. To address this issue, we propose a novel hashing scheme, namely MapEmbed Hashing. Inspired by divide-and-conquer and map-and-reduce, our key idea is named map-and-embed and includes two phases: 1) Map all keys into many small virtual tables; 2) Embed all small tables into a large table by circular move. Our experimental results show that under the same experimental setting, the state-of-the-art perfect hashing (dynamic perfect hashing) can achieve around 15% load factor, around 0.3 Mops update speed, while our MapEmbed achieves around 90% ~ 95% load factor, and around 8.0 Mops update speed per thread. All codes of ours and other algorithms are open-sourced at GitHub.

Sketches, a type of probabilistic algorithms, have been widely accepted as the approximate summary of data streams. Compressing sketches is the best choice in distributed data streams to reduce communication overhead. The ideal compression algorithm should meet the following three requirements: high efficiency of compression procedure, support of direct query without decompression, and high accuracy of compressed sketches. However, no prior work can meet these requirements at the same time. Especially, the accuracy is poor after compression using existing methods. In this paper, we propose Cluster-Reduce, a framework for compressing sketches, which can meet all three requirements. Our key technique nearness clustering rearranges the adjacent counters with similar values in the sketch to significantly improve the accuracy. We use Cluster-Reduce to compress four kinds of sketches in two use-cases: distributed data streams and distributed machine learning. Extensive experimental results show that Cluster-Reduce can achieve up to 60 times smaller error than prior works. The source codes of Cluster-Reduce are available at Github anonymously[1].

Item batch denotes a consecutive sequence of identical items that are close in time in a data stream. It is a useful data stream pattern in cache, burst detection, APT detection, \etc Basic item batch measurement tasks include membership, cardinality, time span and size. Currently, there is no algorithm tailored for item batch measurement. The greatest challenge lies in accurately estimating the time gap between two consecutive identical items. In this paper, we propose Clock-sketch, a framework that introduces the well-known CLOCK algorithm into item batch measurement. The methodology of Clock-sketch is to clean outdated information as much as possible, while guaranteeing that the information of all items visited within the time window $\mathcalT $ is preserved. We conduct experiments on three real-world datasets that feature in item batch pattern. We compare the accuracy and throughput performance of our Clock-sketch against the state-of-the-art and two naive approaches without using Clock-sketch technique. Results of item batch activeness show that Clock-sketch outperforms the state-of-the-art SWAMP in generating 50 times less false positive rate when memory is small. All source codes are open-sourced and released at Github.

Burst is a common pattern in data streams which is characterized by a sudden increase in terms of arrival rate followed by a sudden decrease. Burst detection has attracted extensive attention from the research community. In this paper, we propose a novel sketch, namely BurstSketch, to detect bursts accurately in real time. BurstSketch first uses the technique Running Track to select potential burst items efficiently, and then monitors the potential burst items and capture the key features of burst pattern by a technique called Snapshotting. Experimental results show that our sketch achieves a 1.75 times higher recall rate than the strawman solution.

Data stream processing has become a hot issue in recent years due to the arrival of big data era. There are three fundamental stream processing tasks: membership query, frequency query and heavy hitter query. While most existing solutions address these queries in fixed windows, this paper focuses on a more challenging task: answering these queries in sliding windows. While most existing solutions address different kinds of queries by using different algorithms, this paper focuses on a generic framework. In this paper, we propose a generic framework, namely Sliding sketches, which can be applied to many existing solutions for the above three queries, and enable them to support queries in sliding windows. We apply our framework to five state-of-the-art sketches for the above three kinds of queries. Theoretical analysis and extensive experimental results show that after using our framework, the accuracy of existing sketches that do not support sliding windows becomes much higher than the corresponding best prior art. We released all the source code at Github.

Finding top-k items in data streams is a fundamental problem in data mining. Existing algorithms that can achieve unbiased estimation suffer from poor accuracy. In this paper, we propose a new sketch, WavingSketch, which is much more accurate than existing unbiased algorithms. WavingSketch is generic, and we show how it can be applied to four applications: finding top-k frequent items, finding top-k heavy changes, finding top-k persistent items, and finding top-k Super-Spreaders. We theoretically prove that WavingSketch can provide unbiased estimation, and then give an error bound of our algorithm. Our experimental results show that, compared with the state-of-the-art, WavingSketch has 4.50 times higher insertion speed and up to 9 x 106 times (2 x 104 times in average) lower error rate in finding frequent items when memory size is tight. For other applications, WavingSketch can also achieve up to 286 times lower error rate. All related codes are open-sourced and available at Github anonymously.

Set reconciliation is a fundamental algorithmic problem that arises in many networking, system, and database applications. In this problem, two large sets A and B of objects (bitcoins, files, records, etc.) are stored respectively at two different network-connected hosts, which we name Alice and Bob respectively. Alice and Bob communicate with each other to learn A Δ B , the difference between A and B , and as a result the reconciled set A ∪ B. Current set reconciliation schemes are based on either invertible Bloom filters (IBF) or error-correction codes (ECC). The former has a low computational complexity of O(d) , where d is the cardinality of A Δ B , but has a high communication overhead that is several times larger than the theoretical minimum. The latter has a low communication overhead close to the theoretical minimum, but has a much higher computational complexity of O(d 2 ). In this work, we propose Parity Bitmap Sketch (PBS), an ECC-based set reconciliation scheme that gets the better of both worlds: PBS has both a low computational complexity of O(d) just like IBF-based solutions and a low communication overhead of roughly twice the theoretical minimum. A separate contribution of this work is a novel rigorous analytical framework that can be used for the precise calculation of various performance metrics and for the near-optimal parameter tuning of PBS.

Approximate stream processing has attracted much attention recently. Prior art mostly focuses on characteristics like frequency, cardinality, and quantile. Persistence, as a new characteristic, is getting increasing attention. Unlike frequency, persistence highlights behaviors where an item appears recurrently in many time windows of a data stream. There are two typical problems with persistence - persistence estimation and finding persistent items. In this paper, we propose the On-Off sketch to address both problems. For persistence estimation, using the characteristic that the persistence of an item is increased periodically, we compress increments when multiple items are mapped to the same counter, which significantly reduces the error. Compared with the Count-Min sketch, 1) in theory, we prove that the error of the On-Off sketch is always smaller; 2) in experiments, the On-Off sketch achieves around 6.17 times smaller error and 2.2 times higher throughput. For finding persistent items, we propose a technique to separate persistent and non-persistent items, further improving the accuracy. We show that the space complexity of our On-Off sketch is much better than the state-of-the-art (PIE), and it reduces the error up to 4 orders of magnitude and achieves 2.84 times higher throughput than prior algorithms in experiments.

Finding top-k frequent items has been a hot issue in databases. Finding top-k persistent items is a new issue, and has attracted increasing attention in recent years. In practice, users often want to know which items are significant, i.e., not only frequent but also persistent. No prior art can address both of the above two issues at the same time. Also, for high-speed data streams, they cannot achieve high accuracy when the memory is tight. In this paper, we define a new issue, named finding top-k significant items, and propose a novel algorithm namely LTC to address this issue. It includes two key techniques: Long-tail Replacement and a modified CLOCK algorithm. We theoretically prove there is no overestimation error and derive the correct rate and error bound. We conduct extensive experiments on three real datasets. Our experimental results show that LTC achieves 300~10^8 and in average 10^5 times higher accuracy than other related algorithms.

A graph stream is a continuous sequence of data items, in which each item indicates an edge, including its two endpoints and edge weight. It forms a dynamic graph that changes with every item. Graph streams play important roles in cyber security, social networks, cloud troubleshooting systems and more. Due to the vast volume and high update speed of graph streams, traditional data structures for graph storage such as the adjacency matrix and the adjacency list are no longer sufficient. However, prior art of graph stream summarization, like CM sketches, gSketches, TCM and gMatrix, either supports limited kinds of queries or suffers from poor accuracy of query results. In this paper, we propose a novel Graph Stream Sketch (GSS for short) to summarize the graph streams, which has linear space cost O(|E|) (E is the edge set of the graph) and constant update time cost (O(1)) and supports most kinds of queries over graph streams with the controllable errors. Both theoretical analysis and experiment results confirm the superiority of our solution with regard to the time/space complexity and query results' precision compared with the state-of-the-art.

Cuckoo hashing is widely used for its worst-case constant lookup performance even at very high load. However at high load, collision resolution will involve lots of probes on item relocation and may still fail in the end. To address the problem, we propose an efficient Cuckoo hashing scheme called Multi-copy Cuckoo or McCuckoo. Different from the blind kick-outs of standard Cuckoo hashing during a collision, we can foresee which way to successfully kick items by using multiple copies. Furthermore, with the knowledge of how many copies each item has in the table, we can identify impossible buckets and skip them during a lookup. In order to avoid expensive rehashing during insertion failures, McCuckoo also supports more efficient stash strategy that minimizes stash checking. McCuckoo uses simple logic and simple data structure, so it is suitable for both software and hardware implementation on platforms where intensive access to the slow and bandwidth limited off-chip external memory is the main bottleneck.

Multi-set query is a fundamental issue in data science. When the sizes of multi-sets are large, exact matching methods like hash tables need too much memory, and they cannot achieve high query speed. Bloom filters are recently used to handle big data query, but they cannot achieve high accuracy when the memory space is tight. In this paper, we propose a new data structure named coloring embedder, which is fast, accurate as well as memory efficient. The insight is to first map elements to a high dimensional space to almost eliminate hashing collisions, and then use a dimensional reduction representation, which is similar to coloring a graph, to save memory. Theoretical proofs and experimental results show that compared to the state-of-the[1]art, the error rate of the coloring embedder is thousands of times smaller even with much less memory usage, and the query speed of the coloring embedder is about 2 times faster. The source code of coloring embedder is released on Github.

Data stream processing is a fundamental issue in many fields, such as data mining, databases, network traffic measurement. There are five typical tasks in data stream processing: frequency estimation, heavy hitter detection, heavy change detection, frequency distribution estimation, and entropy estimation. Different algorithms are proposed for different tasks, but they seldom achieve high accuracy and high speed at the same time. To address this issue, we propose a novel data structure named HeavyGuardian. The key idea is to intelligently separate and guard the information of hot items while approximately record the frequencies of cold items. We deploy HeavyGuardian on the above five typical tasks. Extensive experimental results show that HeavyGuardian achieves both much higher accuracy and higher speed than the state-of-the-art solutions for each of the five typical tasks. The source codes of HeavyGuardian and other related algorithms are available at GitHub.

To address the challenge of explosive big data, distributed machine learning (ML) has drawn the interests of many researchers. Since many distributed ML algorithms trained by stochastic gradient descent (SGD) involve communicating gradients through the network, it is important to compress the transferred gradient. A category of low-precision algorithms can significantly reduce the size of gradients, at the expense of some precision loss. However, existing low-precision methods are not suitable for many cases where the gradients are sparse and nonuniformly distributed. In this paper, we study is there a compression method that can efficiently handle a sparse and nonuniform gradient consisting of key-value pairs?

Approximate stream processing algorithms, such as Count-Min sketch, Space-Saving, etc., support numerous applications in databases, storage systems, networking, and other domains. However, the unbalanced distribution in real data streams poses great challenges to existing algorithms. To enhance these algorithms, we propose a meta-framework, called Cold Filter (CF), that enables faster and more accurate stream processing.

Sketch is a data structure used to record frequencies of items in a multiset, which is widely used in data streams, data graph, distributed datasets processing, etc. It works with small memory usage and a high speed at the cost of a slight inaccuracy. In practice, frequencies of items in many datasets are non-uniformly distributed. Unfortunately, existing sketches can hardly work well on non-uniform datasets. To address this issue, we propose a new sketch framework, namely ABC framework, which can be applied to most existing sketches and can significantly improve the accuracy on non-uniform datasets. The key idea behind our framework is that when a counter overflows, it makes use of the space from the adjacent counters by operations of bits-borrowing and combination. Extensive experimental results show that our ABC framework improves the accuracy by 4.10 times and 4.49 times in average, respectively. A demo and all the related source codes are available on our homepage [1].

Hash table, a widely used data structure, can achieve an O(1) average lookup speed at the cost of large memory usage. Unfortunately, hash tables suffer from collisions and the rate of collisions is largely determined by the load factor. Broadly speaking, existing research has taken two approaches to improve the performance of hash tables. The first approach trades-off collision rate with memory usage, but only works well under low load. The second approach pursues high load and no hash collisions, but comes with update failures. The goal of this paper is to design a practical and efficient hash table that achieves high load factor, low hash collision rate, fast lookup speed, fast update speed, and zero update failures. To achieve this goal, we take a three-step approach. First, we propose a set of hashing techniques that leverage Bloom filters to significantly reduce hash collision rates. Second, we introduce a novel kick mechanism to achieve a high load factor. Last, we develop bitmaps to significantly accelerate the kick mechanism. Theoretical analysis and experimental results show that our hashing schemes significantly outperform the state-of-the-art Our hash table achieves a high load factor (greater than 95%), a low collision rate (less than 0.56%), and the number of hash buckets almost equals to the number of key-value pairs. Given n key-value pairs, the collision rate is reduced to 0 by either using 1.18 ×n buckets or allowing up to 5 blind kicks. We have released the source code of the implementations of our hash table and of 6 prior hash tables at Github [1].

A sketch is a probabilistic data structure that is used to record frequencies of items in a multi-set. Sketches have been applied in a variety of fields, such as data stream processing, natural language processing, distributed data sets etc. In this paper, we propose a new sketch, called Slim-Fat (SF) sketch, which has a much smaller memory footprint for query while supporting updates. The key idea behind our proposed SF-sketch is to maintain two separate sketches: a small sketch called Slimsubsketch and a large sketch called Fat-subsketch. The Slimsubsketch enables fast and accurate querying. The Fat-subsketch is used to assist the insertion and deletion from Slim-subsketch. We implemented and evaluated SF-sketch along with several prior sketches and compared them side by side. Our experimental results show that SF-sketch significantly outperforms the most commonly used CM-sketch in terms of accuracy. The full version is provided at arXiv.org [12].

Sketch is a probabilistic data structure, and is used to store and query the frequency of any item in a given multiset. Due to its high memory efficiency, it has been applied to various fields in computer science, such as stream database, network traffic measurement, etc. The key metrics of sketches for data streams are accuracy, speed, and memory usage. Various sketches have been proposed, but they cannot achieve both high accuracy and high speed using limited memory, especially for skewed datasets. To address this issue, we propose a sketch framework, the Pyramid sketch, which can significantly improve accuracy as well as update and query speed. To verify the effectiveness and efficiency of our framework, we applied our framework to four typical sketches. Extensive experimental results show that the accuracy is improved up to 3.50 times, while the speed is improved up to 2.10 times. We have released our source codes at Github [1].

Set queries are fundamental operations in computer systems and applications. This paper addresses the fundamental problem of designing a probabilistic data structure that can quickly process set queries using a small amount of memory. We propose a Shifting Bloom Filter (ShBF) framework for representing and querying sets. We demonstrate the effectiveness of ShBF using three types of popular set queries: membership, association, and multiplicity queries. The key novelty of ShBF is on encoding the auxiliary information of a set element in a location offset. In contrast, prior BF based set data structures allocate additional memory to store auxiliary information. We conducted experiments using real-world network traces, and results show that ShBF significantly advances the state-of-the-art on all three types of set queries.