plurigrid/asi
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Exponential Topology Communication
**Category:** Phase 3 Core - Scalable Communication **Status:** Skeleton Implementation **Dependencies:** `oriented-simplicial-networks` (for topological structure)
SKILL.md
Full skill instructions
Exponential Topology Communication
Category: Phase 3 Core - Scalable Communication
Status: Skeleton Implementation
Dependencies: oriented-simplicial-networks (for topological structure)
Overview
Implements ExpoComm framework for exponentially efficient communication in large-scale systems using hyperbolic embeddings, O(log N) routing, and spectral gap optimization for rapid information dissemination.
Capabilities
- Hyperbolic Embeddings: Embed agents in hyperbolic space
- O(log N) Routing: Greedy routing with logarithmic complexity
- Spectral Gap Optimization: Maximize mixing time via graph structure
- Scalable Broadcast: Efficient all-to-all communication
Core Components
-
Hyperbolic Embeddings (
hyperbolic_embeddings.jl)- Poincaré disk model
- Greedy embedding algorithms
- Distance computation
-
ExpoComm Routing (
expocomm_routing.jl)- Greedy hyperbolic routing
- Load balancing strategies
- Fault tolerance
-
Spectral Optimization (
spectral_optimization.jl)- Graph Laplacian analysis
- Spectral gap maximization
- Expander graph construction
-
Scalability Analysis (
scalability_analysis.jl)- Communication complexity bounds
- Scaling experiments
- Comparison with Euclidean approaches
Integration Points
- Input from:
oriented-simplicial-networks(communication topology) - Output to:
emergent-role-assignment(communication structure influences roles) - Coordinates with:
sheaf-theoretic-coordination(consensus over hyperbolic graphs)
Usage
using ExponentialTopologyCommunication
# Create network of N agents
N = 1000
graph = random_power_law_graph(N, exponent=2.5)
# Compute hyperbolic embeddings
embeddings = hyperbolic_embedding(graph, dim=2)
# Route message from source to target
path = greedy_route(embeddings, source=1, target=N)
@assert length(path) <= 2 * log2(N) # O(log N) guarantee
# Analyze spectral properties
spectral_gap = compute_spectral_gap(graph)
mixing_time = estimate_mixing_time(spectral_gap, N)
References
- Krioukov et al. "Hyperbolic Geometry of Complex Networks" (2010)
- Kleinberg "Navigation in a Small World" (Nature 2000)
- Hoory et al. "Expander Graphs and their Applications" (2006)
Implementation Status
- Basic hyperbolic embeddings
- Greedy routing implementation
- Full spectral gap optimization
- Fault-tolerant routing
- Large-scale benchmarks
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