Query Decomposition: Methods & Applications

• Query Decomposition is the process of breaking complex queries into smaller, manageable subqueries that enable parallel computation and improved system interpretability.
• It employs formal techniques like graph-based dependency modeling and algebraic segmentation to optimize query execution and resource allocation.
• Applications range from LLM-driven reasoning to distributed data retrieval and multimodal search, yielding measurable performance gains and enhanced scalability.

Query decomposition is the process of breaking down a complex query—formulated for information retrieval, database access, reasoning, or interactive services—into smaller, more manageable constituent parts, such as sub-queries, key points, or logical steps. This enables parallel or targeted computation, enhances efficiency, supports pipeline scalability, and often makes it possible to achieve higher quality results under operational constraints. Modern query decomposition methods are central to the runtime performance and interpretability of LLMs and retrieval-augmented systems, as well as in classical graph, logic, and data management frameworks.

1. Formal Approaches to Query Decomposition

Formal query decomposition techniques define precise units and relationships among subcomponents of complex queries, often leveraging graph structures or algebraic formalism. For instance, in dependency-aware settings such as Orion (Gao et al., 28 Oct 2025), a query $Q$ is decomposed into a set $P = \{p_1, ..., p_n\}$ of “key points” together with a directed acyclic graph (DAG) $G=(V, E)$, where each $V_i$ corresponds to $p_i$ and edges encode dependency types $$\tau(i, j) \in \{\mathsf{Null}, \mathsf{Contextual}, \mathsf{Dependent}\}$$. The adjacency matrix $A \in \{0,1\}^{n \times n}$ ensures acyclicity, supporting topological scheduling.

Other domain-specific paradigms include segmenting SQL queries into primitive algebraic operations (Mouravieff et al., 19 Feb 2024), decomposing graph patterns for dynamic search (Choudhury et al., 2014), and modularizing RDF/SPARQL queries into subgraphs or substars for distributed evaluation (Kalogeros et al., 2022, Gai et al., 2015). In model checking, SMT queries can be sliced into independent subformulas for compositional verification (Mrázek et al., 2017).

2. Algorithmic Realizations and Scheduling

The execution of decomposed queries is governed by algorithms that respect both the logical dependencies and the computational architecture. In Orion, the process is split into two phases: (1) key point generation using retrieval-augmented few-shot prompts and (2) logic-parallel content expansion. Here, expansion proceeds by executing each key point in parallel, subject to the dependency DAG, using a concurrent scheduler that triggers node expansion when all parent dependencies are resolved. Prefilling and decoding are separated, with the former compute-bound and the latter memory-bound, allowing for fine-grained pipeline scheduling that exploits hardware utilization up to 90–95% (Gao et al., 28 Oct 2025).

In distributed data systems, query decomposition is tightly connected to minimizing communication overhead and balancing computation. Approaches based on MapReduce or similar frameworks perform local subquery evaluation followed by parallel or staged joins, guided by statistics-driven heuristics for optimal decomposition (Kalogeros et al., 2022, Gai et al., 2015). In dynamic graphs, selectivity statistics inform the ordering and pruning of subquery searches, reducing wasted computation and memory consumption (Choudhury et al., 2014).

3. Applications Across Domains

Query decomposition is pervasive in both neural and classical domains:

• LLM-Augmented Reasoning and Search: Dependency-aware decomposition enables parallel expansion of reasoning steps, improving both end-to-end latency and output quality in high-throughput web and AI assistant services (Gao et al., 28 Oct 2025).
• Product and Item Search: Decomposition of user queries (e.g., extracting superlative semantics and attribute-value “hints”) feeds lightweight rankers for efficient re-ranking in e-commerce retrieval (Zhu et al., 17 Nov 2025).
• Retrieval-Augmented Generation (RAG): Complex user requests are decomposed into atomic subqueries whose document retrieval is governed by multi-armed bandit policies that balance exploration (breadth) and exploitation (precision), resulting in significant precision and $\alpha$-nDCG improvements (Petcu et al., 21 Oct 2025).
• Multimodal Retrieval: Decomposition of video/text queries into latent events or fine-grained aspects enables more effective zero-shot or cross-lingual retrieval, with entropy-based fusion aggregating candidate scores (Dipta et al., 11 Jun 2025, Korikov et al., 1 Aug 2024).
• SQL/Table QA and Semantics: Mapping NL queries to stepwise operator sequences (via QDMR, QPL, or similar formalisms) affords modular training, interpretable execution, and robustness to compositional complexity (Eyal et al., 2023, Mouravieff et al., 19 Feb 2024, Guo et al., 2023).
• Model Checking: Decomposition of symbolic-state formulas drastically reduces existential equivalence checking overhead, as smaller, independent subqueries have higher cache-hit rates and can often be resolved syntactically (Mrázek et al., 2017).
• Quantum Algorithms: Query decomposition takes the form of state decompositions (“block sets”), elucidating the phase structure of query access and enabling explicit linear-algebraic conditions for algorithmic exactness (Grillo et al., 2016).

4. Optimization Criteria and Evaluation

The efficacy of a decomposition method is measured by its impact on efficiency, quality, and scalability. Empirical findings from Orion demonstrate simultaneous token-generation speed-ups (up to $4.33\times$), latency reductions (up to $3.42\times$), and win-rate improvements (up to $18.75\%$) compared to state-of-the-art LLM reasoning strategies (Gao et al., 28 Oct 2025). In RAG and search tasks, adaptive or hint-based decomposition yields 5–10 point absolute gains in MAP/MRR (Zhu et al., 17 Nov 2025, Liu et al., 25 May 2025). In multimodal and multi-aspect retrieval, the correct subdivision of aspects or events dramatically sharpens NDCG and MAP at high imbalance, and per-query analysis confirms the gains are largest when reviews/items are inherently facets-separated (Korikov et al., 1 Aug 2024, Dipta et al., 11 Jun 2025).

Many frameworks include ablation studies showing that decomposition robustness is pivotal under increasing query complexity or distributional skew (Mouravieff et al., 19 Feb 2024, Eyal et al., 2023).

5. Limitations and Trade-offs

Strict dependency modeling, as practiced in Orion and related parallel execution frameworks, introduces a small upfront overhead in key-point generation but prevents coherence loss. However, misclassification of dependencies—particularly by LLM-based classifiers—can lead to expansion stalls or spurious context injection. Fine-grained hardware load balancing remains largely heuristic, with potential for suboptimal SME utilization in multi-query pipelines (Gao et al., 28 Oct 2025).

For semantic decomposition in privacy, there is an inherent trade-off between obfuscity (privacy) and reconstructability (utility); increasing the semantic distance of decomposition improves privacy but may degrade retrieval of intended results (Bollegala et al., 2019).

In distributed graph and data queries, decomposition heuristics such as Min-Res, Max-Degree, and redundancy/reshaping must balance minimizing communication overhead, subquery selectivity, and the number of MapReduce stages. There is no universally optimal scheme: scenarios with high star-like queries may favor redundancy, while more general patterns require layered, statistics-guided decomposition (Kalogeros et al., 2022).

6. Recent Innovations and Extensions

A major trend is leveraging LLMs not only to generate decompositions but to integrate optimization of the decomposition process into the end-to-end performance objectives of the downstream system. POQD, for example, uses an LLM-based prompt optimizer in the loop to search for decomposition strategies that minimize RAG loss, alternating prompt search and model fine-tuning for provable loss improvement (Liu et al., 25 May 2025).

Other extensions include:

• Learned dependency classifiers for edge labeling in execution DAGs (Gao et al., 28 Oct 2025).
• Adaptive granularity, enabling further splitting of heavy substeps for deeper parallelism.
• Quick-feedback user correction for operator pipelines in data analysis authoring tools (Guo et al., 2023).
• Integration of dynamic, on-the-fly retrieval or event-weighting for real-time or counterfactual scenarios (Dipta et al., 11 Jun 2025).

Open challenges include minimizing LLM hallucinations in decomposition, automating error correction, integrating document/image-side decomposition jointly with query decomposition, and scaling methods to deeper, more complex query plans.

7. Impact and Outlook

Query decomposition has become foundational in the design of scalable, efficient, and robust AI reasoning, search, and data systems. Its success is the result of an overview between classical algorithmic and statistical optimization techniques and neural (especially LLM-driven) methods for linguistic, logical, and attributional understanding. As models and datasets scale and query complexity increases, continued advances in decomposition strategies—including automated optimization and hardware-aware scheduling—are expected to underpin the next generation of real-time AI infrastructure and highly interpretable semantic pipelines.

Key references: (Gao et al., 28 Oct 2025, Zhu et al., 17 Nov 2025, Petcu et al., 21 Oct 2025, Dipta et al., 11 Jun 2025, Mouravieff et al., 19 Feb 2024, Eyal et al., 2023, Kalogeros et al., 2022, Gai et al., 2015, Choudhury et al., 2014, Korikov et al., 1 Aug 2024, Mrázek et al., 2017, Grillo et al., 2016, Bollegala et al., 2019, Guo et al., 2023, Brenes et al., 2010, Liu et al., 25 May 2025).