Static Memory Planning

• Static Memory Planning is a set of techniques that assign fixed storage offsets to program objects ahead of execution, optimizing memory usage under constraints.
• It employs methodologies ranging from quick heuristics to ILP and approximation algorithms to minimize fragmentation and improve system performance.
• Applications span deep neural networks, embedded systems, and microarchitecture design, where reducing latency, energy, and runtime overhead is crucial.

Static memory planning encompasses a set of combinatorial optimization techniques for assigning physical storage offsets, banks, or other static memory resource attributes to program objects—such as buffers, tensors, basic blocks, or layouts—prior to execution. The central objective is to minimize overall memory usage, latency, or energy, subject to constraints such as lifetimes, alignment, bank capacity, and access costs. This approach is critical in domains that require predictable operation, reduced runtime overhead, or close adherence to hardware budgets, including embedded systems, deep neural network execution, hybrid DRAM/NVM servers, microarchitecture design, and safe memory management in runtimes.

1. Formal Problem Definitions and Complexity

The archetypal static memory planning problem is dynamic storage allocation (DSA): given a set of $N$ buffers or objects,

$$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$

where $h_i$ denotes the size, and $(t^s_i, t^e_i)$ the exclusive-interval lifetime, the goal is to find offsets $\{ o_i \}$ and contiguous slab size $M$ minimizing

$M = \max_i(o_i + h_i)$

subject to

$$(o_i + h_i \le o_j)\ \text{or}\ (o_j + h_j \le o_i)$$

for all $(i, j)$ with overlapping lifetimes ($t^s_i < t^e_j \wedge t^s_j < t^e_i$).

A key lower bound is the maximum load,

$$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$0

with fragmentation $$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$1. DSA is NP-complete for general $$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$2 and arbitrary overlap patterns. The problem generalizes to bank assignment (with DRAM/NVM), code block placement (flash/RAM), and high-level heap layout.

2. Algorithms and Approaches: From Heuristics to Theoretical Bounds

Static memory planning algorithms stratify into several approaches:

• Heuristics: First-fit, best-fit, “big-rock-first,” and greedy-by-size heuristics rapidly assign offsets but can exhibit poor worst-case fragmentation or scaling.
• Integer/Mixed-Integer Linear Programming (ILP/MIP): Formulations encode lifetimes and non-overlap constraints as binary variables and attain (near-)optimality for moderate $$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$3, harnessing solvers such as GLPK or lp_solve. Examples include basic-block placement in flash vs. RAM (Pallister et al., 2014), DRAM/NVM heap object assignment (Kim et al., 2020), and DNN tensor slotting (Levental, 2022).
• Approximation Algorithms: Techniques developed in theoretical computer science (e.g., Buchsbaum et al., 2003) yield $$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$4–approximate makespans by partitioning objects into height classes (boxing), coloring interval graphs for non-overlap, and recursive subdivision (Lamprakos et al., 7 Apr 2025). These methods, when carefully implemented as in idealloc, scale to $$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$5 buffers with minimal additional fragmentation.
• Stochastic and Bootstrapped Methods: Randomization in tie-breaking, parameter selection, and critical points is used to diversify candidate placements and empirically approach optimality with robustness (Lamprakos et al., 7 Apr 2025).

The table below summarizes key algorithmic paradigms:

Approach	Supported Scale	Guarantees
Greedy/Heuristic	$$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$6	Low planning time, suboptimal fragmentation
ILP/MIP	$$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$7	Near-optimal, exponential time in general
Approximation (idealloc)	$$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$8	$$B = \{ b_i = (h_i,\, t^s_i,\, t^e_i)\;|\;i=1,\ldots,N \}$$9-opt, robust

3. Applications in Compilers and Runtime Systems

Static memory planning is foundational in multiple deployment and runtime settings:

• Deep Neural Networks: MemoMalloc statically allocates a “slab” buffer for all intermediate tensors in a computation graph by capturing allocation lifetimes and resolving possible aliases. The plan is materialized by rewriting TorchScript IR to eliminate per-tensor malloc/free at runtime. MemoMalloc delivers up to 40% inference latency reduction by removing allocator mutex contention, with only moderate (~10–30%) average memory over-provisioning (Levental, 2022).
• Embedded Code-Placement: Compiler ILP post-passes assign hot basic blocks to SRAM rather than flash, balancing energy and timing constraints, and generating branch trampolines for cross-memory transfers. Evaluated on ARM Cortex-M3, average energy drops 7.7% and power drops 21.9%, with some programs achieving 41% power reduction (Pallister et al., 2014).
• Microarchitecture (CPU Dependence Prediction): Static analysis at compile time proves that loads do not alias with any in-flight stores, marking them as “predict no dependency” (PND). Microarchitecture can bypass memory dependence predictor lookups for these loads, eliminating false dependencies, reducing branch rollbacks, and increasing IPC by ~0.7% on small Out-of-Order models (Panayi et al., 2024).
• Hybrid DRAM/NVM Servers: Optimal heap placement across heterogeneous memory media (e.g., DRAM and STT-RAM) under energy constraints employs ILP to assign major objects based on access patterns and predicted energy, outperforming heuristic classification by 14% in energy at iso-latency, and with 4.17× faster planning time (Kim et al., 2020).
• Declarative Heap Layout: High-level layout languages such as Floorplan allow expressive, constraint-based, declarative specification of spatial heap layouts. A constraint solver produces type-safe, statically verified memory mappings, eliminating unsafe pointer arithmetic and boilerplate in runtime systems, as demonstrated for the Immix garbage collector in Rust (Cronburg et al., 2019).

4. Evaluation Methodologies and Metrics

Empirical assessment of static memory planning measures:

• Fragmentation ($h_i$0): $h_i$1, absolute and normalized by $h_i$2, reflects theoretical/potential waste.
• Makespan ($h_i$3): The peak required memory for a plan.
• Robustness: Defined as ability to complete planning within designated wall times (e.g., 15 minutes) on challenging instances.
• Effectiveness-for-Scale: Joint metric combining low fragmentation and completed benchmarks across production allocators and theoretical algorithms (Lamprakos et al., 7 Apr 2025).
• Latency and Throughput: In DNN and runtime systems, empirical wall-clock speedup versus baseline allocator implementations.
• Energy and Power Savings: Board-level and application-level power/energy measurements for embedded and hybrid memory targets.

Benchmark suites span DNN trace logs (minimalloc, MindSpore), distributed workload graphs, and kernel-level heap logs.

5. Theoretical Guarantees, Practical Robustness, and Trade-Offs

Theoretical analysis provides approximation ratios—idealloc achieves

$h_i$4

for suitable choice of $h_i$5. Approaching theoretical minima in practice requires careful attention to latent invariants, such as buffer size distributions and algorithmic bootstrapping. Robust real-world performance is achieved through hybridization: bootstrapping with heuristics, randomized diversification, early-stopping, and parallel decomposition.

Trade-offs include planning time versus optimality, average memory usage versus latency (MemoMalloc), frequency estimation precision versus instrumentation cost (flash/RAM ILP), and static completeness versus runtime adaptivity (static vs. dynamic planners). In policy-driven regions (e.g., DRAM/NVM split), tightening energy constraints leads to smooth performance degradation but strict adherence to budgets (Kim et al., 2020).

Limitations noted in practice involve support for dynamic computation graphs, library code visibility (for code placement), and inter-procedural analysis scalability. Planning for dynamic, multi-model, or distributed workloads remains an open challenge.

6. Extensions, Future Perspectives, and Emerging Trends

Planned and plausible future directions include:

• Dynamic overlays and runtime adaptation: Online reshuffling of objects (e.g., eMDyn in eMap) amortizes migration cost (<5% overhead) to handle budget changes (Kim et al., 2020).
• Global static planning at link time: Enables code/data movement across all program code, removing current per-compilation limitations (Pallister et al., 2014).
• Integration with ML and Hardware Co-design: Static planning as a compiler–microarchitectural interface to signal “safe” behaviors (e.g., PND loads) (Panayi et al., 2024).
• Constraint solver enhancements: SMT-based approaches and richer domain-specific declarative layout languages support flexible, verifiable heap organizations at large scale (Cronburg et al., 2019).
• Meta/Statistical Optimization: For instance, on-the-fly $h_i$6-tuning, critical-point meta-learning within randomized approximation schemes (Lamprakos et al., 7 Apr 2025).
• Multi-model slicing and hierarchically coordinated static plans: For complex, heterogeneous server workloads.

An observed trend is the convergence of static memory planning with high-level symbolic reasoning, hardware/ISA cooperative design, and large-scale DNN inference/deployment pipelines, driven by the scaling of modern memory-bound workloads and increasing hardware/energy heterogeneity.

7. Summary Table: Representative Static Memory Planning Systems

Domain	Method/Theory	Exemplary System	Key Metric	Reference
DNN inference	Greedy+MIP, interval	MemoMalloc	Up to 40% latency gain	(Levental, 2022)
Embedded systems	ILP, cost model	GCC/LLVM post-pass	Up to 41% power savings	(Pallister et al., 2014)
Heap allocation	ILP (DRAM/NVM)	eMap (eMPlan)	14% energy reduction	(Kim et al., 2020)
DSA scaling	Approximation (boxing)	idealloc	$h_i$7 excess frag., $h_i$8	(Lamprakos et al., 7 Apr 2025)
Heap layout	Declarative constraint	Floorplan	87% “unsafe” code reduction	(Cronburg et al., 2019)
Hardware design	Static analysis mark-up	PND-loads (OoO-CPU)	0.5–0.7% IPC improvement	(Panayi et al., 2024)

In conclusion, static memory planning unifies theoretical combinatorial optimization, high-performance system implementation, energy/power-aware placement, and safe, maintainable runtime design. The discipline is central to scaling general-purpose computing into increasingly fragmented and resource-constrained environments, and continues to integrate advances from programming languages, compiler analysis, and hardware–software co-design.