god-graph 0.6.0-alpha

A graph-based LLM white-box optimization toolbox: topology validation, Lie group orthogonalization, tensor ring compression
Documentation
# God-Graph Performance Benchmark Report

> Test Date: 2026-03-27
> Test Environment: Linux, 61GB RAM, Multi-core CPU
> God-Graph Version: v0.4.0-beta

## Executive Summary

God-Graph is a high-performance Rust graph operation library featuring bucket-based adjacency list layout, arena-style slot management, and parallel computing optimizations. Benchmark results show:

- **Parallel PageRank**: Achieves **80x speedup** on 1000-node graph (Serial 53.9ms → Parallel 668µs)
- **Parallel Connected Components**: 357µs on 2000-node graph
- **Parallel Degree Centrality**: 68µs on 5000-node graph
- **Doctest Pass Rate**: 100% (27/27 passed)
- **Clippy Warnings**: 0

**Note**: This library uses a bucket-based adjacency list variant (named CsrStorage in code) instead of traditional CSR format to support O(1) incremental updates. Parallel algorithms use fine-grained locks (Mutex/RwLock) to protect shared data. par_dijkstra is marked as experimental in v0.3.0-beta.

## Test Environment

| Item | Configuration |
|------|---------------|
| Operating System | Linux |
| Memory | 61GB |
| Rust Version | 1.85 (2021 edition) |
| Compile Optimization | `-C opt-level=3 -C lto=thin -C codegen-units=1` |

## Parallel Algorithm Speedup

### PageRank

| Nodes | Serial Time | Parallel Time | Speedup |
|-------|-------------|---------------|---------|
| 1,000 | 53.9 ms | 668 µs | **80.7x** |
| 5,000 | 1.68 s | Pending | Pending |

**Test Parameters**: damping=0.85, iterations=20, avg_degree=5

**Analysis**: PageRank algorithm in God-Graph achieves significant speedup, mainly due to:
1. Reverse adjacency list optimization, time complexity O(iterations × E)
2. Parallel node updates under fine-grained lock protection
3. Bucket-based adjacency list provides efficient neighbor traversal

### Connected Components

| Nodes | Parallel Time | Notes |
|-------|---------------|-------|
| 200 | 35.8 µs | 4 components |
| 400 | 66.5 µs | 4 components |
| 1,000 | 147.8 µs | 4 components |
| 2,000 | 357.8 µs | 4 components |

**Test Parameters**: Sparse graph (ring-like), each component forms a ring + extra edges

**Note**: Parallel union-find implementation may not show significant speedup on multi-core CPUs because union-find operations are inherently serial. Current implementation uses atomic CAS operations for safety, with path compression removed to avoid race conditions.

### Degree Centrality

| Nodes | Parallel Time |
|-------|---------------|
| 500 | 27.0 µs |
| 1,000 | 49.1 µs |
| 2,000 | 68.9 µs |
| 5,000 | Pending |

**Test Parameters**: avg_degree=10

## Memory Layout Optimization

### Bucket-Based Adjacency List

God-Graph uses a bucket-based adjacency list variant (named CsrStorage in code) instead of traditional CSR to support O(1) incremental updates:

```rust
pub struct AdjBucket {
    neighbors: Vec<usize>,      // Target node indices
    edge_indices: Vec<usize>,   // Edge indices
    deleted_mask: Vec<u64>,     // Bitmap for lazy deletion
    deleted_count: usize,       // Deletion counter
}

pub struct CsrStorage {
    buckets: Vec<AdjBucket>,           // Adjacency bucket per node
    reverse_buckets: Vec<AdjBucket>,   // Reverse adjacency (directed graph)
    needs_compact: bool,               // Compaction flag
}
```

**Advantages**:
- O(1) incremental edge insertion (push to bucket)
- Lazy deletion (deleted_mask bitmap)
- On-demand compaction (compact() reclaims space)
- 64-byte alignment avoids false sharing
- Software prefetching support (conditional compilation nightly)

### Arena-style Slot Management

```rust
pub struct NodeSlot<T> {
    data: Option<T>,
    generation: u32,
}

pub struct Graph<T, E> {
    nodes: Vec<NodeSlot<T>>,
    edges: Vec<EdgeStorage<E>>,
    csr: CsrStorage,
    free_nodes: Vec<usize>,  // Free list
    free_edges: Vec<usize>,
}
```

**Features**:
- generation validation prevents ABA problems
- Free list supports index reuse
- Contiguous slot storage optimizes cache hit rate

## Algorithm Performance Comparison

### Traversal Algorithms

| Algorithm | Implementation | Time Complexity | Parallel |
|-----------|----------------|-----------------|----------|
| DFS | Recursive + Iterative | O(V+E) ||
| BFS | Queue | O(V+E) ||
| Tarjan SCC | Iterative | O(V+E) ||

### Shortest Path Algorithms

| Algorithm | Implementation | Time Complexity | Parallel |
|-----------|----------------|-----------------|----------|
| Dijkstra | Priority Queue | O((V+E)logV) | ✓ (delta-stepping) |
| Bellman-Ford | Iterative | O(VE) ||
| Floyd-Warshall | Dynamic Programming | O(V³) ||
| A* | Heuristic Search | O((V+E)logV) ||

### Centrality Algorithms

| Algorithm | Implementation | Time Complexity | Parallel |
|-----------|----------------|-----------------|----------|
| Degree Centrality | Counting | O(V) ||
| Betweenness Centrality | Brandes Algorithm | O(VE) ||
| Closeness Centrality | BFS | O(V(V+E)) ||
| PageRank | Iterative | O(iterations×E) ||

### Maximum Flow

| Algorithm | Implementation | Time Complexity | Memory Optimization |
|-----------|----------------|-----------------|---------------------|
| Edmonds-Karp | BFS Augmenting Path | O(VE²) | O(V+E) Adjacency List |
| Dinic | Layered Graph | O(V²E) | O(V+E) Adjacency List |
| Push-Relabel | Preflow Push | O(V²E) | O(V+E) Adjacency List |

**Memory Optimization**: Flow algorithm residual graph changed from `Vec<Vec<f64>>` adjacency matrix to `Vec<Vec<(usize, f64)>>` adjacency list, space complexity reduced from O(V²) to O(V+E).

## Test Coverage

### Unit Tests

- **Total**: 88
- **Pass Rate**: 100%

### Integration Tests

- **Total**: 18
- **Pass Rate**: 100%

### Property Tests

- **Total**: 15
- **Pass Rate**: 100%

### Doctests

- **Total**: 27
- **Pass Rate**: 100%
- **Ignored**: 0

### Clippy

- **Warnings**: 0 (23 fixed)

## Comparison with petgraph

| Feature | God-Graph | petgraph |
|---------|-----------|----------|
| CSR Format | ✓ (Bucket-based) | ✓ (Traditional) |
| Incremental Updates | ✓ O(1) | ✗ Requires rebuild |
| Generation Validation |||
| Parallel Algorithms | ✓ (5+) ||
| 64-byte Alignment |||
| Software Prefetching | ✓ (nightly) ||
| Community Maturity | 🌱 Growing | 🌳 Mature |

**God-Graph Advantages**:
1. Generation-indexed stability prevents ABA problems
2. Bucket-based adjacency list supports O(1) incremental updates
3. Parallel algorithm suite (PageRank, BFS, DFS, Connected Components, Degree Centrality)
4. Cache optimization (64-byte alignment, software prefetching)

**petgraph Advantages**:
1. Mature community, production-proven
2. Documentation completeness
3. More algorithm variants

**Architecture Notes**:
- God-Graph uses bucket-based adjacency list (named CsrStorage in code), not traditional CSR format
- Parallel algorithms use fine-grained locks (Mutex/RwLock), not lock-free design
- par_dijkstra is marked as experimental in v0.3.0-beta with known issues

## Pending Work

### Performance Optimization

- [ ] SIMD vectorization optimization (PageRank score batch computation)
- [ ] par_dijkstra refactoring (fix bucket index calculation errors and deadlock risks)
- [ ] Fine-grained lock optimization (reduce Mutex contention overhead)
- [ ] More complete speedup data (especially for large graphs)

### Documentation

- [ ] petgraph migration guide (framework created)
- [ ] Production environment case collection
- [ ] Algorithm visualization examples

### Testing

- [ ] Large-scale graph tests (100K+ nodes)
- [ ] Memory usage benchmarks
- [ ] Concurrency safety tests

## Conclusion

God-Graph core functionality has reached **v0.4.0-beta** standard, with known issues to be fixed:

✅ All clippy warnings fixed (0)
✅ Doctest 100% pass rate (27/27)
✅ Unit tests, integration tests, property tests all passing (121/121)
✅ Parallel algorithm speedup data support (PageRank 80x)
✅ Core architecture correctly implemented (bucket-based adjacency list, generation validation, cache optimization)

⚠️ **Known Issues**:
- par_dijkstra has bucket index calculation errors and deadlock risks, marked as experimental
- Parallel algorithms use fine-grained locks (Mutex/RwLock), not lock-free design
- Bucket-based adjacency list (named CsrStorage in code) is not traditional CSR format

**Recommendation**: Prioritize fixing P0 issues (documentation integrity and par_dijkstra bugs), then release v0.4.0-beta to collect user feedback. Subsequent optimization focus on SIMD vectorization and larger-scale benchmarks.

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*Last Updated: 2026-03-27*