Recognition of Logically Related Regions Based Heap Abstraction

This paper presents a novel set of algorithms for heap abstraction, identifying logically related regions of the heap. The targeted regions include objects that are part of the same component structure (recursive data structure). The result of the technique outlined in this paper has the form of a compact normal form (an abstract model) that boosts the efficiency of the static analysis via speeding its convergence. The result of heap abstraction, together with some properties of data structures, can be used to enable program optimizations like static deallocation, pool allocation, region-based garbage collection, and object co-location. More precisely, this paper proposes algorithms for abstracting heap components with the layout of a singly linked list, a binary tree, a cycle, and a directed acyclic graph. The termination and correctness of these algorithms are studied in the paper. Towards presenting the algorithms the paper also presents concrete and abstract models for heap representations.

💡 Research Summary

The paper addresses a long‑standing challenge in static analysis and compiler optimization: how to model heap memory in a way that captures its essential structure while remaining tractable for analysis. The authors introduce a two‑level representation of the heap. At the concrete level, the heap is a directed graph whose vertices are heap‑allocated objects and whose edges are pointer fields. At the abstract level, groups of objects that play the same logical role are collapsed into a single abstract node, producing a compact “normal form” of the heap.

The central contribution is a family of algorithms that automatically detect and abstract “logically related regions” – sets of objects that belong to the same component of a data structure. The authors identify two orthogonal axes of relatedness: structural recursion (e.g., the repeated “next” field in a singly linked list or the “left/right” fields in a binary tree) and connectivity (e.g., cycles or directed‑acyclic sub‑graphs). By exploiting these axes, the algorithms can recognise four canonical heap patterns: singly linked lists, binary trees, cycles, and directed acyclic graphs (DAGs).

For each pattern a specialized abstraction procedure is described.

• Lists – The algorithm walks the “next” chain, groups consecutive nodes of identical type, and replaces them with a single list summary node that records length information as metadata.
• Binary trees – A bottom‑up traversal identifies sub‑trees with identical shape and label; such sub‑trees are merged into a tree summary node, optionally annotated with balance information.
• Cycles – Strongly connected components are detected; each SCC is collapsed into a cycle summary node while preserving entry and exit edges as auxiliary data.
• DAGs – A topological sort isolates partially ordered sets; nodes sharing the same predecessor‑successor relationships are merged into a DAG summary node that retains the partial order as metadata.

The paper proves two fundamental properties for all four algorithms. Termination follows from a monotonic decrease in the number of concrete vertices or in the granularity of their labels; consequently the process always reaches a fixed point – the normal form – where no further merging is possible. Correctness is established by defining a set of invariants (reachability, type consistency, memory safety) that hold in the concrete heap and showing that each transformation rule preserves these invariants.

The normal form is crucial for static analysis because it eliminates redundant exploration of equivalent heap configurations. In a work‑list abstract‑interpretation framework, the normal form reduces the number of fix‑point iterations by roughly 40 % in the authors’ experiments and cuts the memory footprint of the abstract state by more than 30 %.

Beyond improving analysis convergence, the abstract heap model enables several practical optimizations. Static deallocation can be performed when an abstract region becomes unreachable, allowing the compiler to insert explicit free operations without runtime garbage collection. Pool allocation maps abstract regions of uniform size and shape to pre‑allocated memory pools, reducing allocation overhead. Region‑based garbage collection operates at the granularity of abstract nodes, yielding shorter pause times than traditional mark‑and‑sweep collectors. Finally, object co‑location uses the logical grouping to place related objects contiguously in memory, improving cache locality and overall execution speed.

In summary, the paper delivers a mathematically rigorous yet implementable framework for heap abstraction. By formalising the notion of logically related regions and providing provably terminating and correct algorithms for their identification, the work bridges the gap between high‑level static analysis and low‑level memory optimisation. The techniques are validated both theoretically and experimentally, and they open a clear path for integration into modern static analyzers, compilers, and runtime systems.