core/topology.rs - Knowledge Structure Topology System Abstract

High-Level Purpose

Comprehensive graph-based knowledge representation system supporting multiple topology types (linear, cyclic, DAG, general graphs) for modeling structured learning domains with sophisticated path finding and relationship analysis capabilities.

Key Data Structures and Relationships

  • Topology: Central graph structure with type-specific optimizations
  • Node: Knowledge elements with labels, positions, and unique identifiers
  • Edge: Directed relationships with weighted connections between knowledge elements
  • TopologyType: Enumerated topology variants with specialized algorithms
  • Node Mapping: Efficient lookup structures for label-to-index resolution

Main Data Flows

  • Graph Construction: Type-specific graph building with validation and optimization
  • Path Finding: Dijkstra's algorithm for shortest path computation in weighted graphs
  • Relationship Queries: Successor/predecessor relationships and distance calculations
  • Traversal Operations: Topological sorting, segment extraction, and path enumeration
  • Comparative Analysis: Node ordering and relationship comparisons across topology types

External Dependencies

  • serde: Serialization support for graph persistence and transmission
  • std::collections: HashMap, HashSet, VecDeque for efficient graph algorithms

State Management Patterns

  • Immutable Structures: Read-only graph structures after construction
  • Efficient Indexing: Pre-computed node mappings for O(1) lookup operations
  • Type-Specific Optimization: Specialized algorithms for different topology types

Core Algorithms and Business Logic Abstractions

  • Graph Algorithms: Dijkstra's shortest path, topological sorting, BFS traversal
  • Distance Metrics: Type-specific distance calculations (linear, cyclic, graph-based)
  • Relationship Analysis: Path existence, comparability, and ordering relationships
  • Segment Operations: Sequential element extraction with directional support
  • Validation Logic: Graph structure validation and consistency checking

Topology Types and Applications

  • Linear Topology: Sequential structures like alphabets and ordered lists
  • Cyclic Topology: Circular structures like days of week and periodic sequences
  • Partial Order (DAG): Hierarchical dependencies and prerequisite relationships
  • General Graph: Arbitrary weighted networks with complex interconnections

Knowledge Domain Support

  • Alphabet Learning: 26-letter linear structure with position-based operations
  • Temporal Sequences: Cyclic structures for time-based learning
  • Skill Dependencies: DAG structures for prerequisite learning paths
  • Arbitrary Domains: Flexible graph structures for complex knowledge representations

Performance Optimizations

  • Pre-computed Indices: O(1) node lookup through hash-based indexing
  • Type-Specific Algorithms: Optimized algorithms for each topology type
  • Memory Efficiency: Compact representation with minimal overhead
  • Algorithm Selection: Automatic algorithm selection based on topology type