EmbeddingGemma 2: an open, lightweight multimodal embedding model
deepmind.google·6d ago
AI Engineering
Lobsters·27d ago·5 min read
Search over Algebraic Graphs
TL;DR
A method for executing Dijkstra’s algorithm directly on algebraic graph representations has been developed, eliminating the need for adjacency maps. This approach achieves a time complexity of O(s log s), where s is the size of the graph expression.
✦ Why It Matters
Consider implementing this direct approach to improve the efficiency of your graph algorithms today.
Key Takeaways
- Utilize algebraic graph representations for efficient graph operations.
- Implement the indexing system to avoid adjacency map overhead.
- Run Dijkstra's algorithm directly on algebraic graphs.
- Achieve O(s log s) time complexity for graph searches.
How It Works
The proposed method builds an index while traversing the algebraic graph, storing relationships between nodes without expanding the graph into an adjacency map. This index allows for efficient neighbor retrieval during Dijkstra's search, enabling the algorithm to operate directly on the compressed graph structure.