Pointer Chasing Problem

Updated 2 September 2025

Pointer chasing is the process of recursively dereferencing pointers to determine reachable memory locations, foundational for program analysis and hardware optimization.
The technique employs abstract interpretation and flow-sensitive points-to analysis to safely over-approximate pointer chains and detect potential runtime errors.
In hardware and communication complexity, pointer chasing informs prefetcher design and underpins tight lower bounds, highlighting its impact on performance and theoretical models.

The pointer chasing problem is a foundational concept at the intersection of programming languages, static analysis, hardware architecture, and communication complexity. It describes the process of dynamically following one or more levels of pointer dereferences—so-called "chasing pointers"—to reach a target location or value in memory. This process is central both in the implementation and analysis of heap-manipulating programs (especially in low-level languages like C/C++) and in the paper of interactive computation models, such as two-party communication protocols and streaming algorithms. Rigorous paper of the pointer chasing problem has led to precise formalizations, static analysis techniques, hardware-level optimizations, and strict lower bounds in computational complexity.

1. Formal Definitions and General Setting

In its classic form, the pointer chasing problem can be framed either as a program analysis task or as a communication complexity problem.

Program Analysis Perspective: Given a set of program statements involving pointer assignments and dereferences (e.g., chains like $p \rightarrow *p \rightarrow **p$ ), the pointer chasing problem asks: What set of memory locations can be reached by repeatedly dereferencing a pointer variable, possibly conditioned on control flow and dynamic memory allocation? The analysis must conservatively over-approximate all concrete executions due to undecidability in non-trivial languages (0810.0753).
Communication Complexity Perspective: In a canonical two-party or multi-party scenario, two (or more) players are given functions or tables (e.g., arrays $a,b \in [n]^n$ or functions $N_A, N_B\colon [n] \to [n]$ ). Starting from a fixed position, the players alternately "chase" pointers defined by their respective functions for $k$ steps, with the goal of determining the endpoint or some property of the resulting value. The central computational question is: What is the minimum amount of communication (in bits) required between the players to correctly compute the outcome, as a function of $n$ and $k$ (Fischer et al., 26 Aug 2025, Mao et al., 17 Nov 2024, Viola, 11 Jul 2025)?

2. Static Analysis and Verification: Points-To and Abstract Interpretation

The pointer chasing problem is central to points-to analysis and alias analysis in static program analysis.

Store-Based, Flow-Sensitive Points-To Analysis: (0810.0753) presents a formalized points-to analysis for C-like languages, defining memory as a function from locations to locations, and capturing points-to relations as sets of pairs (abstract memory). Pointer chasing is recursively modeled by an evaluation function, e.g.,

$\epsilon\text{val}(A, l) = \{l\},\qquad \epsilon\text{val}(A, *e) = \text{post}(A, \epsilon\text{val}(A, e))$

with $A$ denoting the abstract memory relation. This setup enables modeling of multi-level dereferences.

Abstract Interpretation and Soundness: Abstract interpretation is used to construct a lattice of possible program states and to prove, via Galois connections, that the analysis soundly over-approximates all possible pointer chains. Formally, for an abstract memory $A$ , the concretization function $\gamma(A)$ captures all possible concrete memories subsumed by $A$ . Abstract evaluation, assignment, and filtering operations are rigorously proven to be sound:

$\bigcup_{C\in\gamma(A)} \epsilon\text{val}(C, e) \subseteq \epsilon\text{val}(A, e)$

Precision via Filter Operations: The introduction of control-flow-sensitive filters allows the removal of infeasible paths from the abstract points-to set, increasing precision in identifying possible pointer targets along a chase, especially across conditionals (0810.0753).
Applications: This analysis is critical in software verification (proving absence of null dereferences, buffer overflows, etc.) and enables proving data structure invariants that rely on following pointer chains to their endpoints.

3. Hardware Acceleration: Prefetching Pointer Chains

The pointer chasing problem presents unique challenges and opportunities in microarchitecture design, particularly for cache-unfriendly data structures.

Limitations of Traditional Caches: Linked data structures (lists, trees) often have poor spatial locality, rendering conventional caches ineffective for traversal workloads.
Pointer-Chase Prefetcher: (Srivastava et al., 2018) introduces a hardware/software cooperative mechanism—the pointer-chase prefetcher—that exploits compile-time information. Through a special instruction (e.g., lw.cp), the processor signals that a load is a pointer chase load. When executed, this instruction
- Fetches the immediate target node,
- Immediately calculates and prefetches the next node indicated by the fetched pointer,
- Employs hardware buffers and FSM control logic for speculative look-ahead.

The effect is to overlap memory latency of subsequent dereferences, significantly reducing cache miss penalties for pointer-chasing workloads. With minimal area and energy overhead, up to 30% performance improvements are observed on benchmarks traversing linked structures.

Dependence on Compiler Hints: The effectiveness of this technique relies on explicit hints from the compiler to annotate pointer-chaseable accesses, ensuring that prefetching is targeted and effective.

4. Communication Complexity and Lower Bounds

Pointer chasing has emerged as a canonical hard problem in interactive communication models, serving as the backbone for lower bounds in streaming and distributed algorithms.

Classical Model: In a $k$ -step pointer chasing scenario, Alice and Bob alternately apply their private mappings to an index, with the goal of computing the final output. The cost is the total number of bits exchanged to compute the output with bounded or zero error.
Round-Communication Trade-offs and Gadgetless Lifting: (Mao et al., 17 Nov 2024) establishes essentially tight lower bounds for the $(k-1)$ -round distributional communication complexity of $k$ -step pointer chasing on uniform inputs:

$CC(II) = \Omega\left(\frac{n}{k} + k\right)$

via a "gadgetless lifting" framework, which shows that the lower bound for restricted (coordinate-wise/informationally local) protocols lifts to general protocols through structure-vs-pseudorandomness decompositions. This matches the previous upper bound of $O(n/k + k)$ and removes the additional $k\log n$ loss present in prior round elimination methods.

Round Elimination and Fixed-Set Lemma: (Viola, 11 Jul 2025) provides a concise proof of the $n/8$ lower bound for deterministic $k$ -round protocols using the fixed-set lemma. At each step, heavily biased (non-"alive") pointers are fixed to their most popular value, increasing the effective density and enabling round elimination. The proof is inductive, showing that protocols below this communication volume lead to contradiction as pointer "density" exceeds permissible bounds.
Unlimited Interaction: (Fischer et al., 26 Aug 2025) studies protocols with no restrictions on the number of rounds, showing that even in this setting, the total communication is bounded below by

$\Omega\left( k \log\frac{n}{k} \right)$

for constant-error randomized protocols, and by $\Omega(k\log\log k)$ for zero-error protocols. Hence, the trivial $k$ -round protocol is optimal up to constant factors, demonstrating the inherent lack of parallelizability in pointer chasing due to its sequential dependencies.

Hidden-Pointer Chasing and Streaming Lower Bounds: (Assadi et al., 2019) introduces a variant—hidden-pointer chasing—where the pointers themselves are hidden within separate set intersection communication problems. This increases the lower bound from linear to nearly quadratic in $n$ when the number of communication phases is limited, and enables strong lower bounds for graph streaming (e.g., minimum $s$ – $t$ cut requires $\Omega(n^2/p^5)$ space for $p$ passes).

5. Model Checking, Separation Logics, and Verification Frameworks

Pointer chasing is central to software verification, including model checking and reasoning with separation logics.

Bounded Model Checking with Expressive Logics: (Charatonik et al., 2016) shows that error conditions (e.g., dereference of dangling pointers) in heap-manipulating programs can be captured with a combination of two-variable first-order logic (with counting) and inductive Datalog predicates. This enables expressing and verifying heap reachability, pointer equality, aliasing, and absence of leaks within a decidable logic fragment, and covers complex pointer-chasing scenarios (e.g., intersecting list segments).
Heap Separating Points-To Logic: (Haberland et al., 2019) presents a formalism for reasoning about pointer chains using heaplets (local heap fragments), heap conjunction (∘), and heap inversion. The logic enforces separation and compositionality, allowing local verification of pointer chasing properties and supporting efficient SMT-based checking. Algebraic properties (identity, associativity, inversion) facilitate modular verification of complex chains.
Modern Efficient Pointer Analysis: (Kuderski et al., 2019) introduces TeaDsa, a scalable LLVM-based analysis that avoids oversharing of abstract objects between procedures, introduces partial flow sensitivity, and incorporates type awareness to improve precision. These features directly enhance the accuracy of pointer chasing, reducing spurious aliases and scaling to large codebases.

6. Applications and Broader Implications

The pointer chasing problem, in both analysis and complexity forms, has wide-ranging implications.

Application Domain	Role of Pointer Chasing	Key Results/Impacts
Static program analysis and verification	Determines reachable memory locations, finds bugs, verifies data invariants	Flow-sensitive, abstract-interpretation-based analyses; increased soundness/precision (0810.0753, Kuderski et al., 2019)
Compiler and system optimization	Guides alias analysis, loop optimization, parallelization barriers	Analysis precision enables safe optimizations
Microarchitecture for performance	Drives hardware/software co-design for cache-unfriendly workloads (linked lists)	Pointer-chase prefetchers with compiler hints (Srivastava et al., 2018)
Streaming/lower bound proofs	Serves as canonical hard problem embedding sequentiality in communication	Tight multi-pass lower bounds for graph problems (Mao et al., 17 Nov 2024, Assadi et al., 2019)
Formal verification/model checking	Enables precise specification/checking of heap properties via spatial logics	Automated shape analysis, heap property decidability (Charatonik et al., 2016, Haberland et al., 2019)

The pointer chasing problem remains a pivotal concept in theoretical and applied computer science. Its complexity-theoretic hardness, shaped by inherent dependencies in pointer chains, limits parallelization and informs lower bounds across models. Its foundational role in static program analysis underlies much of the machinery for dependable software systems. Finally, hardware-level and verification advances targeting pointer chasing directly influence the efficiency, correctness, and security of modern software and architectures.