Algorithms
Key algorithms used in ƒxyz Network
Three categories of algorithms run on the network graph: pathfinding for currency routing, cycle detection for arbitrage, and search for information retrieval.
Core Algorithm Categories
Graph Algorithms
Bellman-Ford and line-graph pathfinding for optimal multi-hop currency conversion. Community detection (Louvain, spectral) for cluster identification in the membership and currency graphs.
Arbitrage Algorithms
These algorithms detect price variances across markets and platforms, identifying rate discrepancies through graph-based analysis of currency pair relationships.
Search Algorithms
Information retrieval across the graph database and market data feeds.
Technical Implementation
These algorithms work together to build the computational layer of the network:
- Optimizing routes for cross-market currency conversion
- Detecting rate discrepancies across currency pair graphs in real time
- Enabling fast data retrieval from graph databases and market feeds
- Processing complex financial relationships through network analysis
Learn More
For detailed technical specifications, implementation details, and specific algorithm architectures, see:
- Technology Stack: Complete technical documentation
- Graph Data Systems: Neo4j implementation details
- Network Foundations: High-level algorithm overview
References
- Dijkstra, E.W. "A note on two problems in connexion with graphs." Numerische Mathematik 1(1), 1959 - Foundational shortest-path algorithm
- Bellman, R. "On a Routing Problem." Quarterly of Applied Mathematics 16(1), 1958 - Negative cycle detection for arbitrage
- Hart, P.E., Nilsson, N.J. & Raphael, B. "A Formal Basis for the Heuristic Determination of Minimum Cost Paths." IEEE Trans. SSC 4(2), 1968 - A* search algorithm
- Holland, J.H. Adaptation in Natural and Artificial Systems. University of Michigan Press, 1975 - Genetic algorithms
- Duan, R. et al. "Breaking the Sorting Barrier for Directed Single-Source Shortest Paths." STOC 2025 Best Paper - First sub-Dijkstra SSSP algorithm in 41 years
- Markowitz, H. "Portfolio Selection." Journal of Finance 7(1), 1952 - Mean-variance optimization
For the detailed algorithm specifications with code references, see the Algorithm Reference.
Foundations
Core principles, governance logic, token model, compliance posture, and historical first principles behind the ƒxyz Network.
Magnitude Aspect
How the Harvard spectral sequence — O / B / A / F / G / K / M — places every member on a temperature-grounded stellar class. The canonical magnitude aspect, locked v1.0.