From Batch to Stream: Automatic Generation of Online Algorithms (2404.04743v2)

Abstract: Online streaming algorithms, tailored for continuous data processing, offer substantial benefits but are often more intricate to design than their offline counterparts. This paper introduces a novel approach for automatically synthesizing online streaming algorithms from their offline versions. In particular, we propose a novel methodology, based on the notion of relational function signature (RFS), for deriving an online algorithm given its offline version. Then, we propose a concrete synthesis algorithm that is an instantiation of the proposed methodology. Our algorithm uses the RFS to decompose the synthesis problem into a set of independent subtasks and uses a combination of symbolic reasoning and search to solve each subproblem. We implement the proposed technique in a new tool called Opera and evaluate it on over 50 tasks spanning two domains: statistical computations and online auctions. Our results show that Opera can automatically derive the online version of the original algorithm for 98% of the tasks. Our experiments also demonstrate that Opera significantly outperforms alternative approaches, including adaptations of SyGuS solvers to this problem as well as two of Opera's own ablations.

• The paper introduces a novel methodology using Relational Function Signatures to automate the conversion of offline batch algorithms into online streaming algorithms.
• The implemented tool, Opera, successfully synthesized online algorithms for 98% of tasks in statistical and auction domains, outperforming existing synthesis methods.
• This automated conversion enables accessible and efficient stream processing solutions for applications dealing with large, evolving datasets like real-time analytics and financial trading.

Essay on "From Batch to Stream: Automatic Generation of Online Algorithms"

The paper "From Batch to Stream: Automatic Generation of Online Algorithms" presents a novel approach to automating the transformation of offline batch-processing algorithms into their online streaming counterparts. The work specifically addresses the challenge of synthesizing online streaming algorithms, which process data incrementally as it arrives, thus offering significant performance benefits over offline algorithms that require the entire dataset upfront.

Key Contributions

1. Relational Function Signature (RFS): The authors introduce the concept of an RFS, which serves as a critical relational specification connecting the offline and online algorithms. The RFS effectively maps each auxiliary parameter of the online algorithm to expressions in the offline algorithm, thus guiding the synthesis process.
2. Synthesis Methodology: The methodology leverages RFS to ensure that the online algorithm is inductive relative to the offline version. The paper provides a concrete, sound, and, under certain conditions, complete synthesis procedure that involves:
   • Inferring an RFS from the offline version.
   • Constructing an initializer to compute initial values for the online algorithm.
   • Synthesizing the online algorithm to maintain the RFS relationship through data increments.
3. Decomposition and Expression Synthesis: The synthesis process is decomposed into generating a sketch with placeholders for expressions dependent on the streaming data. These placeholders are then synthesized independently using a combination of symbolic reasoning (such as quantifier elimination) and search-based techniques.
4. Tool Implementation and Evaluation: The methodology is implemented in a tool called Opera. The tool is evaluated on more than 50 conversion tasks from two domains: statistical computations and online auctions. Opera successfully synthesizes online versions of algorithms with a success rate of 98%, demonstrating its efficacy and performance advantage over existing techniques, including adapted general-purpose synthesis tools like CVC5 and Sketch.

Methodological Insights

The approach hinges on the use of RFS, which is an important conceptual advancement in specifying the relationship between batch and stream processing. By focusing on maintaining a relational invariant, the authors ensure that the synthesized algorithm retains the logical equivalence to its offline counterpart while benefiting from the incremental nature of online processing.

The use of symbolic reasoning to derive expressions for online programs represents a significant enhancement, addressing the practical challenge of synthesizing correct and efficient algorithms in a compositional manner. The integration of enumerative synthesis with symbolic methods allows Opera to handle complex expressions that arise in real-world applications, such as statistical variance computations.

Implications and Future Directions

The research presents practical implications for domains dealing with large, evolving datasets, such as real-time data analytics and financial trading platforms. By automating the conversion from offline to online algorithms, the paper paves the way for accessible, efficient solutions in stream processing.

Theoretical implications include the exploration of synthesis techniques that marry symbolic and search-based methods, enhancing the capability to handle a broad range of synthesis tasks. Future work could extend this approach to incorporate approximate algorithms, which are often necessary when streaming constraints make exact computation impractical.

The authors also highlight the challenges posed by highly complex expressions, like those encountered in kurtosis calculations, and the potential limitations of the current symbolic methods. Enhancing the algorithm's ability to tackle such problems remains an open area for research, potentially through the integration of advanced algebraic techniques or hybrid heuristic-guided synthesis approaches.

In summary, this paper provides a robust framework for systematically converting offline algorithms to incremental online formats, showcasing the potential for automated program synthesis techniques to fundamentally transform data processing methodologies in various high-impact domains.