Atree: A simple and efficient pointer-free tree implementation
An array-based, “pointer-free” tree structure called Atree is prompting debate over whether indices into flat vectors really offer performance and cache-locality advantages versus traditional pointer-based trees. Supporters highlight benefits for specific workloads—such as compilers, scientific computing, and GPU- or SIMD-style batch operations—where trees are traversed linearly or mostly read-only and compact, contiguous storage can give large speedups. Critics counter that Atree’s O(n) child lookups, lack of inherent ordering, and reliance on index-chasing make it inferior to established cache-aware trees (like B‑trees or Eytzinger layouts) for many real-world, dynamically updated hierarchies, arguing that careful choice of data structure and empirical benchmarking matter more than avoiding pointers per se.
Overall Design & Intended Use
- Atree represents a tree as flat arrays with parent indices (struct-of-arrays, “pointer-free” in the sense of no raw language pointers).
- Goals: cache locality, fewer allocations, easier serialization, compatibility with array/vector-style processing, and possible GPU friendliness.
- Several commenters note this style is already common in specific domains (heaps, disjoint sets, ECS trees, skeletal animation hierarchies, scientific trees).
Performance, Big-O, and Practical Trade-offs
- Major criticism: getting children of a node is O(N) via full scan, seen as a nonstarter for many workloads, especially large trees.
- Defenders argue:
- For many passes (e.g., compiler-style full sweeps, or workloads where N is small and bounded), O(N) scans are acceptable or even efficient.
- Big-O alone can mislead; constant factors, cache behavior, and I/O patterns often dominate.
- Critics reply that for large trees, scanning the whole structure per child query is not realistic, and better asymptotics matter.
- Debate over vector/SIMD style: if operations are over “all nodes at once,” a single O(N) pass for all children may be fine; if you need children of a single node repeatedly, it’s poor.
Cache Locality, Indices vs Pointers
- Many note that integer indices are effectively pointers; main benefits:
- Indices can be smaller, better packed, and easily serialized or passed over the network.
- Entire structure can live in one contiguous block, improving cache hits.
- Counterpoint: “index-chasing” still has the same cache-miss character as pointer-chasing if access patterns are irregular.
- General agreement that cache-friendly layout is about contiguity and access patterns, not merely avoiding language pointers.
Alternative and Extended Structures
- Mentioned alternatives: Eytzinger (implicit) trees, cache-oblivious B-trees, B/B+ trees, van Emde Boas layouts, pool/arena-allocated pointer trees.
- Suggestions to extend Atree:
- Add first-child/next-sibling indices instead of (or in addition to) parent.
- Pack children together, possibly sorted, at the cost of O(N) inserts (memmove).
- Maintain explicit leaf arrays with auxiliary index maps for O(1) leaf add/remove.
- Limitation noted: Atree as presented has no inherent ordering or locality among siblings; ordering children or making ordered traversals efficient requires extra invariants and complexity.