Datapath-Structure-Aware Partitioning

• Datapath-Structure-Aware Partitioning Strategies are methodologies that analyze datapath properties to optimize division of complex tasks across heterogeneous systems.
• They employ a two-phase workflow combining static control-data flow analysis with dynamic profiling to extract key metrics like operator mix and execution frequency.
• Empirical validations in hardware mapping, graph analytics, and SAT-based verification demonstrate significant improvements in throughput, cycle reduction, and solver efficiency.

Datapath-Structure-Aware Partitioning Strategies are methodologies that leverage specific properties of computational datapaths—such as operator mix, arithmetic regularity, critical path topology, and execution profiles—to optimize the division of large, complex tasks (e.g., hardware design, graph processing, dataflow computation) across heterogeneous resources or parallel engines. Unlike generic approaches, these strategies extract, analyze, and exploit datapath characteristics at the program, circuit, or graph level to inform how subtasks are mapped, scheduled, or distributed for maximal performance, balanced load, and tractable verification.

1. Foundational Concepts and Methodologies

Datapath-structure-aware partitioning first requires rigorous characterization of “datapath structure.” In hybrid reconfigurable platforms, this includes the bit-width, operator mix (e.g., ALU, multiplier ratio), execution frequency, and intra-block data dependencies of each basic computational unit (e.g., basic block, circuit region, graph vertex). The partitioning workflow typically consists of two main stages: an analysis phase and a partitioning/mapping phase.

In the analysis stage, control-data flow graphs (CDFG) are built from source code (C/C++ or hardware IR), followed by static inspection to count operator types and their bit-widths. Dynamic profiling instruments execution (e.g., using counter insertion) to gather basic block frequencies under real workloads. The combined “weight” (often denoted $total\_weight(BB)$) is used to rank hotspots for acceleration or offloading (0710.4844).

For distributed graph analytics, feature extraction collects moment statistics of degree distributions (mean $\mu_d$, variance $\sigma^2_d$, skewness $\gamma_d$, kurtosis $\kappa_d$), structural flags, and algorithmic operator counts (e.g., GET_IN, APPLY, ARITH_OPS) to build a compact feature vector. This representation enables model-driven partitioning decisions that are sensitive to both graph topology and computational requirements (Park et al., 2022).

In combinational equivalence checking (CEC) for datapath circuits, structure-aware partitioning involves extracting XOR-chain regularity in CNFs derived from arithmetic blocks, computing topological scores for cut variables, and recursively splitting subproblems along optimal “structural” boundaries (Zhang et al., 7 Dec 2025).

2. Taxonomy of Partitioning Strategies

Datapath-structure-aware strategies are instantiated across various domains:

• Hybrid reconfigurable platforms: Partitioning between fine-grained (FG) FPGA fabric (configurable logic blocks, LUTs) and coarse-grained (CG) ASIC-style datapaths (ALUs, multipliers), directed by operator counts, loop frequencies, and area/time models (0710.4844).
• Graph analytics: Edge-cut and vertex-cut partitioners, hybrid streaming (PowerLyra, HDRF), and greedy strategies are selected according to extracted graph and algorithm features. Machine learning models predict execution times per strategy and automate selection (Park et al., 2022).
• Dataflow systems: Node placement and schedule are informed by critical path up/down ranks; partitioners (CP, Batch Split, MITE, DFS) allocate operators to devices based on structural rank and communication cost, often seeking to minimize global makespan (Mayer et al., 2017).
• SAT-based hardware verification: Regularity-aware splitting minimizes SAT solver stall on XOR-heavy arithmetic blocks by scoring and selecting cut-points spatially distributed in the circuit, leveraging both input/output proximity and chain length (Zhang et al., 7 Dec 2025).

The following table summarizes distinctive strategy families in the context of graph partitioning:

Strategy Family	Feature Sensitivity	Typical Algorithms
Edge-cut	Out-degree uniformity, push/pull	1D-Src, Hybrid
Vertex-cut	Degree skew, hub spreading	HDRF, 2D, Ginger
Hybrid/Streaming	Dynamically tunable, application-specific	PowerLyra, Random

3. Algorithmic Details and Structural Feature Extraction

The implementation of structure-aware partitioning requires multi-level analysis:

In hybrid SoC partitioning (0710.4844):

• Static: $bb\_weight = \sum w_{OP}$ for all operations in a basic block.
• Dynamic: $total\_weight(BB) = exec\_freq(BB)\cdot bb\_weight$.
• Sorted ranking identifies critical kernels for migration to CG datapath.
• Partitioning engine iteratively moves BBs, recomputes $t_{total} = t_{FG} + t_{CG} + t_{comm}$, and terminates when timing/area constraints are met.

In graph analytics (Park et al., 2022):

• Extract graph-level features: $$(|V|, |E|, \mu_d, \sigma^2_d, \gamma_d, \kappa_d, \delta_{dir})$$.
• Algorithm features: counts of high-level graph operations, arithmetic operator density.
• Training: XGBoost regression models for each strategy, using synthetic aggregation to expand training data.
• Prediction: Run-time feature extraction and runtime selection based on minimum predicted execution time.

In circuit SAT verification (Zhang et al., 7 Dec 2025):

• Boolean propagation applied to partial assignments, with extraction of XOR chains.
• For candidate cut variables $v$, compute $$sc(v) = |c|^2 / (\alpha \cdot dis_O[v] + (1-\alpha) \cdot dis_I[v] + 1.0)$$, smoothed by local graph propagation.
• Select the maximum-scoring $v$ for expansion in dynamic divide-and-conquer SAT tree.

4. Empirical Performance and Trade-offs

Experimental validations demonstrate substantial throughput and efficiency gains:

• In OFDM transmitter and JPEG encoder mapping (0710.4844), relocating a few top-ranked BBs from FG to CG datapath meets tight timing constraints with up to 82% cycle reduction. Smaller FG area (AFPGA) budgets benefit most from structure-aware partitioning.
• In large-scale graph analytics (Park et al., 2022), ML-based strategy selection was within 5.4% of the absolute optimum and 1.456× faster than random mean strategy across 528 tasks; key features (degree skew, pull/push operator density) drove strategy selection, with HDRF or 2D preferred for high-skew graphs and edge-cut/hybrid sufficing for uniform degree.
• TensorFlow graph partitioning with critical-path-focused heuristics (Mayer et al., 2017) yielded up to 4× speedup over hash-based and FIFO baselines, with the CP partitioner and scheduler delivering the shortest makespan, especially for communication-bound models.
• FastLEC (Zhang et al., 7 Dec 2025) showed a 19× speedup for pure SAT solves on XOR-heavy sub-miters at 128 core parallelism; the full hybrid engine solved all 368 benchmarks 14.6× faster than prior best, validating dynamic splitting along datapath-regular boundaries.

5. Theoretical Guarantees and Completeness

The structure-aware partitioning framework for SAT-based equivalence checking preserves completeness via Shannon expansion:

$F \equiv (F \land v) \lor (F \land \neg v)$

Each recursive partition covers mutually exclusive assignment spaces; unsatisfiability across all leaves implies unsatisfiability of the original CNF, ensuring soundness and completeness (Zhang et al., 7 Dec 2025). This expansion principle generalizes to other partitioning domains whenever fixed-point coverage of decision space or resource allocations can be formally justified.

6. Practitioner Guidance and Applied Insights

Effective deployment of datapath-structure-aware partitioning requires:

• Rigorous extraction of operator counts, bit-widths, and execution profiles (e.g., in DSP mapping (0710.4844)).
• Quantitative analysis of graph features (degree statistics, iteration intensity) to choose edge/vertex cut strategies (e.g., favoring HDRF for highly skewed graphs (Park et al., 2022)).
• Use of ranking metrics (upRank, downRank, totalRank) to prioritize global critical paths for dataflow operator placement and scheduling (Mayer et al., 2017).
• Structure scoring (e.g., chain length, cut proximity) as a basis for dynamic problem decomposition in SAT-based verification (Zhang et al., 7 Dec 2025).
• Machine-learning strategy selection, aggregating historical run logs and synthetic combinations to enhance model robustness (Park et al., 2022).

Common patterns include the importance of dynamic re-evaluation, iterative migration of hotspots, and coupling between analysis phase (data and algorithm feature extraction) and mapping algorithms. Shared cost models govern trade-offs between area, cycle time, communication overhead, and solver parallelization.

7. Cross-Domain Impact and Future Directions

Structure-aware partitioning principles have been successfully applied in hybrid hardware mapping (0710.4844), distributed graph analytics (Park et al., 2022), parallel dataflow frameworks (Mayer et al., 2017), and formal circuit verification (Zhang et al., 7 Dec 2025). Their convergence informs future directions in:

• Automated hardware/software codesign, with partitioning workflows embedded in high-level synthesis.
• Self-tuning distributed analytics frameworks, adapting to graph and algorithmic features at runtime.
• Scalable, structure-guided SAT solving for arithmetic/logic-heavy circuits.
• Integration of ML-based predictors and feature extractors into runtime schedulers and partitioners.

A plausible implication is that as system heterogeneity and problem complexity increase, unified approaches that combine structural analysis, analytic cost modeling, and data-driven strategy selection will be increasingly critical for scalable design, verification, and distributed computation.