The data streams generated by IoT devices have distinct characteristics that pose specific challenges for processing [6]:

I. Continuous: data is continuously generated and received over time. SP pipelines must be able to handle these continuous data streams from different sources.

II. High volume: IoT devices generate a massive volume of data streams. The number of connected IoT devices is growing exponentially, with projections showing billions of devices worldwide. Working with large amounts of streaming time-series data can be a challenging task.

III. High speed: data can be received at high speeds and at different flow rates. IoT data volumes must be transferred to cloud servers at maximum speed to provide real-time information.

IV. Diversity: data can come from different sources in different formats, from IoT sensors to social networks.

This diversity encompasses numerical values, text, images, sounds, videos, or a combination of these, which increases the complexity of processing.

V. Temporal component: data often has a temporal component, which means the evolution of one or more variables over time. This characteristic creates the need to preserve the order of the data, handle out-of-order data, and use time windows for more accurate analysis, especially in forecasting problems.

However, real-time processing of this data is not always straightforward. The large volume of data generated by IoT can lead to transmission collisions and energy waste due to data redundancy. Additionally, since devices may be vulnerable to security attacks or malfunctions, or unexpected events may occur, methods for detecting anomalies in data streams are crucial.

IoT devices, especially small sensors deployed in various environments, are often challenging to charge after deployment, resulting in significant energy waste. Processing and transmitting data from these devices is expensive and consumes a lot of bandwidth, energy, and time. Resource-constrained IoT devices have limited computational resources. These constraints necessitate new approaches that strike a balance between computational efficiency and acceptable accuracy, while also ensuring system performance and energy efficiency [7].

Traditional computing methods used in these devices are plagued by high energy consumption and low performance. Therefore, novel approaches such as AC techniques are essential for building a new generation of low-power IoT devices. By balancing computational efficiency with acceptable accuracy, AC offers significant improvements in energy efficiency, speed, and area for resource-constrained IoT devices. Specific examples of energy-saving strategies and resource-relief strategies in IoT include the use of BFs, 6T SRAM, Dynamic Voltage/Frequency Scaling (DVFS) management techniques, IoT approximate processors, in-memory computing, and DRAM refresh rate tuning. Despite these advances, sensor devices still face significant challenges in terms of energy consumption, cost, throughput, and accuracy. Optimal energy utilization is critical for time-sensitive applications enabled by WSNs. Traditional static sink-based approaches in WSNs suffer from energy inefficiency, high latency, and uneven load distribution, with nodes close to the sink draining energy faster and creating “Energy holes.” Hence, dynamic sink-based strategies are needed to optimize mobility, balance energy, and minimize query response time.

The rapid adoption of IoT devices and the increasing advancement of Artificial Intelligence (AI) underscore the growing importance of processing IoT data streams at the network edge and integrating AI into them [11]. Edge AI, which is a combination of edge computing and AI, not only changes the way data is processed but also opens up unprecedented opportunities for various application scenarios [12]. AI enables autonomous data analysis and decision-making directly on edge devices, thereby reducing the dependency on cloud servers. This makes the processing of many traditional applications that were previously difficult relatively simple. AI-based edge computing is crucial for optimizing decision-making in various IoT applications:

I. In everyday life, autonomous driving is a prime example, where AI models on vehicle equipment make driving decisions using sensor data processed through edge computing technology.

II. Smart furniture, such as cameras and home robots, uses AI and edge computing to provide personalized services and security.

III. In the industrial IoT environment, the combination of edge computing and AI plays a vital role in production lines, enabling equipment failure monitoring and prediction and preventive maintenance.

However, the actual deployment of edge AI still faces many challenges. These challenges include limited computing resources on edge devices, which are generally less than those of cloud servers. Implementing large and complex AI models on edge devices requires developing larger and more efficient models, as well as considering hardware accelerators. Energy efficiency of edge computing is also a challenge, as most devices rely on battery power, and highly optimized AI algorithms can still generate significant energy consumption. In the context of processing data streams generated by IoT devices, the need for fast query response is critical, especially in real-time environments. Approximate Query Processing (AQP) emerges as a crucial strategy for overcoming the challenge of efficiently processing large, high-speed data streams while providing timely query responses [13]. AQP operates on the principle of sacrificing a degree of accuracy in exchange for increased performance and improved energy efficiency. This approach is particularly beneficial for applications where absolute, precise results are not strictly required or where a certain degree of imprecision can be tolerated without significantly impacting the overall outcome. Key techniques used in AQP to achieve this balance include:

I. Sampling: involves analyzing a representative subset of data rather than processing the entire data set, which can significantly reduce computational complexity and speed up processing time.

II. Sketching: use of PDS to summarize large data sets in a quantitative space, providing approximate answers to queries with probabilistic error bounds. Examples include BFs for Approximate Membership Queries (AMQ), Count-Min Sketch (CMS) for frequency estimation, and HyperLogLog (HLL) for cardinality estimation.

III. Aggregation-based approaches: perform aggregation operations on summarized data (such as samples or sketches) rather than on the raw data. Data aggregation in IoT sensor networks is critical to reducing data redundancy and saving energy.

AQP finds significant applications in big data visualization. As the size of data sets increases, traditional visualization models struggle to provide fast, efficient, and interactive representations. Approximate visualization techniques, such as those based on sampling, bridge the gap between massive amounts of data and interactive presentation by accelerating the process and increasing performance.

As a result, edge computing, edge AI, and AQP are critical to enabling efficient, low-latency, secure, and energy-aware processing of the massive data streams generated by IoT devices. By moving computation and decision-making to the data source, they address key challenges of centralized cloud architectures and unlock the full potential of real-time IoT applications across various domains.

To overcome the challenge of limited resources while still supporting fast queries on large data streams, PDS offers an attractive solution. PDSs are data structures that provide approximate answers to queries, typically with a probabilistic guarantee of error, while utilizing significantly less memory and computational resources than deterministic data structures that provide exact answers. They are particularly well-suited for scenarios where a level of inaccuracy is acceptable in exchange for a significant increase in performance.

A BF is a space-efficient PDS used to test whether an element is a member of a set [14]. A key feature of BFs is that they may yield false positives (indicating the presence of a component when it is not) but never false negatives (an aspect that is in the set is always reported as present). This one-sided error guarantee is critical in many applications. BFs are renowned for their compactness and efficiency in determining membership and are widely utilized in various fields, including IoT, networking, databases, and bioinformatics. Their space efficiency and fast membership queries make them valuable in scenarios where memory is a significant constraint. In the context of IoT, BFs are widely used, especially in wearable electronics, where battery life is a considerable concern.

A recently proposed class is the Learned Bloom Filter (LBF), which combines the CBF with a learning model LBF aims to provide the same one-sided error guarantee as CBF but with potentially better performance for the same memory budget [15]. A Standard Learned Bloom Filter (SLBF) uses a learning model as a prefilter before a supporting CBF. The supporting CBF is queried only for inputs that the learning model predicts are not in the set, which ensures that the critical completeness property (no false negatives) is maintained throughout the entire structure.

While efficient, the use of BFs in IoT and other applications also raises concerns about privacy. Research has shown that CBCs can be vulnerable to set reconstruction attacks, where an attacker with access to the internal state of the filter may be able to infer the original set with high probability. Addressing the privacy of data stored in a BF has been identified as a significant open problem. Recent work provides a detailed differential privacy-based analysis of BFs. It is also noted as the first work to analyze and address the privacy of learned BFs under any exact model. Privacy-preserving algorithms, such as Nickel and Dime [16], have been proposed based on random response mechanisms. These algorithms modify the input set stored by the BF rather than modifying the internal state. Nickel adds privacy without compromising the one-way error guarantee of BF, while Dime introduces a significant trade-off in terms of false negative probability.

Challenges in BF design include managing the trade-off between the false positive rate and memory space, selecting optimal hash functions, accommodating their predefined size that is difficult to change for large or growing datasets, and handling element deletion. Despite these challenges, efforts continue to refine these structures for better performance and security in resource-constrained environments. An enhanced Bloom filter (eBF) has been developed specifically for intrusion detection in IoT networks, demonstrating significant memory savings over standard BFs and other variants while maintaining fast and accurate performance. A lightweight BF accelerator for IoT applications has also been implemented using hardware such as FPGAs. It is.

Beyond BFs, several other data structures are well-suited to handling the continuous and often extensive nature of data streams, particularly those used in AQP and data summarization. Sketching data structures is a family of structures designed to summarize large data sets in a small amount of space [17]. They are valuable for providing approximate answers to queries and for data compression. Sketching-based data structures are a common technique for estimating frequencies in data streams, including the Count Sketch (CS), the CMS, and the Count-Mean-Min Sketch (CMMS). For example, the Count-Min Sketch effectively trades off accuracy for a significant reduction in memory consumption, making it a powerful solution for estimating item frequency in large datasets where precise storage is impossible. However, CMS can suffer from overestimation due to hash collisions, and its accuracy depends on the quality of the hash functions used. Count-Sketch is a viable alternative that supports decrement operations and negative counts, which CMS lacks. These constructs are critical for querying continuous data streams with limited resources, as they maintain compact summaries for efficient estimation of query results.

Another important PDS is the HLL. HLL is a mighty approximation algorithm used to estimate the cardinality (number of unique elements) of a large set [18]. It provides reasonably accurate estimates with much less memory than methods that require storing all elements. HLL is utilized in network monitoring, web analytics, data analysis, and database management. Like CMS, HLL has limitations, such as not supporting element deletion; however, variants like the sliding HLL address this problem. An extension called KHyperLogLog (KHLL) is used to estimate re-identifiability and joinability risks in large databases.

Processing massive, continuous data streams can be applied at different levels of the hardware stack to improve the performance of IoT applications:

Circuit level: a critical focus is on redesigning basic arithmetic units such as adders, multipliers, and dividers. These units are central to many fault-tolerant applications. By designing approximate versions, significant reductions in power consumption, area, and latency can be achieved. Examples include various types of approximate adders, multipliers, and dividers. Hardware implementations of primitive and activation functions, which are critical to many algorithms, including those used in IoT, also benefit from approximation techniques. Approaches such as lookup tables, polynomial approximation, shift-and-add algorithms (such as CORDIC), and hybrid methods are employed, often sacrificing speed/area for improved accuracy [19]. Architecture level: design of specialized approximate processing units and memory systems is essential.

I. Approximate memory: techniques are being explored to make memory systems more energy efficient. These include voltage scaling for SRAMs, reducing refresh rates for DREAMs, and compressing or encoding data before storage. These methods leverage fault tolerance in applications. For IoT devices, especially those that rely on battery power or operate with limited memory, approximate memory designs such as fault-tolerant configurable SRAMs and refresh-free DRAM techniques are being developed.

II. Approximate processors and accelerators: these are integrated units designed with controlled imprecision to increase computational efficiency. Low-power architectures such as ARM and open source RISC-V are being explored for IoT approximate processors, specifically for tasks such as machine learning. Accelerators such as TPUs, which use reduced precision, represent an architectural approach.

III. DVFS management: techniques such as DVFS, Voltage Over Scaling (VOS), dynamic power management (DPM), and near-threshold voltage (NTV) operation are widely used in IoT to save energy. These methods use idle times or reduce voltage/frequency at the cost of potential faults, which can be managed in fault-tolerant applications.

Data level (hardware aspects): the use of approximate data types and data structures directly affects the hardware requirements for storage and manipulation. Techniques such as precision scaling (using fixed-point or floating-point with lower precision) and quantization reduce memory and computational costs. These are critical for deploying models on resource-constrained edge devices. Hardware accelerators such as GPUs and TPUs are designed to handle reduced-precision formats efficiently.

AC also impact algorithm design, making them suitable for implementation on resource-constrained IoT hardware:

Software level: algorithms can be designed or modified to introduce approximations into their code. This includes identifying non-critical computations where accuracy can be degraded. Techniques include computation skipping (e.g., perforation loops or selective skipping of instructions), iterative refinement (early stopping iterations), function approximation (replacing exact functions with approximate functions, possibly using neural networks), pruning (removing redundant parts of models such as neural networks), and lazy synchronization in parallel algorithms to reduce waiting times. These methods trade off performance and error. Approximate memoization techniques can store and reuse approximate results for similar inputs, reducing redundant computation.

Data level (algorithmic aspects): designing algorithms that operate on approximate data representations is key. Data sampling algorithms analyze representative subsets of large datasets or streams to provide faster, approximate results with defined error bounds. PDSs are inherently algorithmic and are designed for approximate queries with minimal memory overhead. BFs are used for approximate membership testing, while sketch data structures (e.g., CMS, HLL) are employed for frequency estimation and cardinality counting in data streams, and MinHash is used for set similarity estimation. These structures enable efficient data processing and summarization on devices with limited resources.

Effective use of AC for IoT often requires a cross-layer co-design approach, integrating techniques at the hardware, architecture, software, and data levels. Frameworks and tools are being developed to support this, helping designers manage the trade-off between accuracy and efficiency and automating the process of identifying approximation opportunities and applying techniques. For example, Approximate Logic Synthesis (ALS) tools automate the design of approximate digital circuits.

In essence, AC enables the design of specialized and resource-efficient hardware components and systems, while also guiding the development of algorithms that can operate effectively with controlled imprecision on these limited platforms. This dual effect is critical to enabling the deployment of complex data processing and AI tasks on the growing number of IoT devices.

applications, power- (controllable), design in power arithmetic units constrained IoT complexity consumption, area (adders, multipliers, devices, digital and latency approximate circuits dividers), elementary functions/approxim ate activation (lookup tables, CORDIC)

Resource- Controlled Energy efficiency, Approximate Architecture constrained IoT inaccuracy, potential computational memory (SRAM devices, machine errors, verification efficiency, reduced voltage scaling, learning at the edge, challenges memory footprint DRAM refresh rate battery-life-critical reduction), applications approximate processors/accelerat ors (low-power IoT processors, reduced-precision TPUs), DVFS management

Deploying AI Loss of accuracy, Reduced memory Precision scaling Data (Hardware models on edge need for hardware and computing (fixed/floating point Aspects) devices, processing support costs, efficient with lower big data storage precision), quantization algorithms, analytical coding complexity reduced overhead, loop perforation), programs faster execution time iterative refinement (early stopping iterations), function approximation, pruning, lazy synchronization, approximate memoization[7] Data flow analysis, Possible errors, Faster approximate Data sampling Data (Algorithmic approximate queries, controlled results, minimal algorithms, PDS Aspects) resource-constrained imprecision, need memory overhead, such as BFs (for devices, membership for optimal hash efficient data membership testing, frequency functions processing/summari queries), sketching estimation zation structures such as CMS (for frequency/cardinalit y estimation), MinHash

AC (AxC) is a growing paradigm that strategically trades off accuracy in exchange for higher performance (speed, energy efficiency, memory footprint). This approach is particularly well-suited for resource-constrained IoT environments and fault-tolerant applications. The following table compares high-level approaches to AC based on their level of abstraction, standard techniques, main advantages, trade-offs, and application areas, using information provided in the references.

Despite advances in approximate computation and efficiency paradigms, several challenges remain, especially when applied to the dynamic and resource-constrained nature of IoT:

I. Scalability, security, and privacy in IoT data SP: the rapid adoption and development of IoT devices is leading to the growing trend of edge computing, which is changing the way data is processed. Edge computing brings more innovative solutions to various application scenarios in IoT. However, the resource and energy efficiency of edge computing has certain limitations. With the increasing use of IoT end devices, a massive amount of sensor data is being generated. Managing this significant volume of data is a major challenge. Data centers, such as cloud computing storage spaces, are struggling to provide the necessary resources for transmission due to the explosion in data volume. The growing number of connected IoT devices is increasing exponentially. This growth brings new challenges for data processing and transmission.

Security and privacy issues are significant concerns in IoT environments. The integration of edge computing and AI can significantly enhance the data privacy and security concerns that are of most concern to individuals. Edge computing enables local data processing, reduces the transmission of sensitive data, and thereby enhances data security. Edge computing provides unprecedented opportunities for many application scenarios, including improved data privacy and secure management. Strong security measures are increasingly necessary in applications such as autonomous driving, innovative furniture, and industrial automation. Existing decentralized architectures for large-scale IoT networks have not consistently addressed security and privacy concerns. Traditional cloud servers employ a centralized architecture that connects IoT devices for processing and storage, which can lead to transmission issues, security vulnerabilities, or a single point of failure. A decentralized architecture is required to manage security and energy-related issues in IoT-based networks. Blockchain technology has been widely researched due to its decentralized nature and its potential to protect IoT devices from security threats and rogue service providers.

The security implications of approximation computations, especially in sensitive applications, require careful consideration. AC can complicate reverse engineering, but it can also introduce new target areas for hardware trojans in circuits that control approximation levels. Assessing the security of approximation circuits is challenging because their defenses against passive side-channel attacks can vary with voltage-frequency settings. Approximation circuits may be vulnerable to fault injection attacks, especially at operational limits, although the full effects and effectiveness of countermeasures are still unclear. Processing-In-Memory (PIM) introduces changes to security models due to architectural modifications, programming models, side-channel vulnerabilities, device reliability concerns, and potential hardware trojans. Developing secure and privacy-preserving AC methods is a critical area of future research.

II. Heterogeneous and incomplete data management: anomaly detection in bright environments, often based on IoT data streams, is challenging due to complex dynamics. Commonly encountered challenges include scarcity (e.g., lack of labeled data, unbalanced datasets) and complexity (e.g., noisy data, high dimensionality, conceptual drift). Contextualization challenges arise from the need to consider complex relationships between influencing factors to distinguish abnormal events from regular events under specific conditions. Data streams can originate from various sources in different formats, making their processing unwieldy, especially in real-time applications. The diversity of data that can be received increases the complexity of working with big data. Managing out-of-order and delayed data is a fundamental challenge in SP.

Data transmission delays due to distributed sensors and diverse communication channels are a critical challenge in industrial IoT anomaly detection, making models essential to account for these delays to ensure accurate real-time detection. Managing the temporal aspects of data, particularly the order of streams and handling out-of-order data, is crucial for accurate and timely data analysis. Integrating stored (historical) and streaming data is also a key aspect of data management.

III. Ensuring Quality of Service (QoS) in dynamic environments: satisfying Quality of Service (QoS) under workload changes has been a long-standing research challenge in SP systems. Stream processors lack control over the rate of incoming events and must be adaptable to handle the load. Ensuring predictable results and maintaining real-time response are essential requirements for real-time SP. Scalability, the ability of a system to handle growing workloads without compromising performance, is critical and can be achieved through scale-in, scale-out, and scale-up strategies.

Fault tolerance and rapid recovery are crucial for maintaining high availability and data integrity in SP. Consistent SP is an open research problem due to the challenging nature of processing unbounded streams in a distributed setting. High availability is addressed through various replication approaches.

Approximate computations essentially involve a trade-off between accuracy and efficiency (speed and energy consumption). Managing this trade-off is a key challenge in approximate programming. For approximate memory, a careful evaluation is necessary to achieve a balance between the benefits of minimizing accuracy and the degree of precision required for a particular application. ALS faces the challenge of accommodating varying accuracy requirements while managing power and delay variations. Designing high-quality, configurable circuits that can be tuned to different levels of accuracy in real-time is required.

In dynamic WSN scenarios, the computational efficiency of query processing relies on lightweight optimization approaches that ensure consistency. Ensuring efficient and reliable data delivery services, as well as longer network lifetime, are critical issues in mobile sensor networks. This requires a balance between efficient data transmission and energy conservation.

Based on the current landscape and existing challenges, several promising avenues for future research emerge: