Scalable Routing via Greedy Embedding and Random Projection
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Solution Overview
Problem
The scalability of routing systems is hindered by the exponential growth of BGP routing tables, and existing geometric routing methods require accurate node locations and large coordinate sizes, which do not effectively address the issue of scalability.
Innovation Solution
A method for scalable routing using greedy embedding, where a graph topology is embedded into a geometric space with log(n) coordinates, allowing for efficient greedy forwarding by projecting nodes into a k-dimensional space with random projection, reducing the size of the routing table to polylogarithmic dimensions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Kleinberg's hyperbolic plane embedding is used for greedy routing, then routing scalability is improved, but the coordinate size requires n bits per node which increases memory usage
Solution Approach 1:
The patent transforms the routing problem from n-dimensional hyperbolic space to a lower-dimensional Euclidean space while preserving greedy routing properties. This dimensional reduction allows coordinates to be represented with fewer bits, directly addressing the memory usage issue while maintaining routing scalability.
Solution Approach 2:
The patent changes the coordinate representation parameters from n-bit hyperbolic coordinates to polylogarithmic-sized Euclidean coordinates. This parameter transformation reduces the space complexity from O(n) to O(polylog(n)), resolving the contradiction between scalability and memory efficiency.
2Productivity
If geometric routing based on actual node location is used, then routing efficiency is improved, but accurate knowledge of node location is required which increases system complexity
Solution Approach 1:
The patent introduces virtual Euclidean coordinates as an intermediary representation that captures essential topological relationships without requiring precise physical location data. This intermediary coordinate system enables efficient greedy routing while avoiding the complexity of accurate location tracking.
Solution Approach 2:
The patent creates a simplified copy of the network topology in the form of Euclidean coordinates that approximate node positions. This coordinate copy preserves enough structural information for efficient routing without requiring the full complexity of actual node locations.
3Adaptability or versatility
If virtual geographic coordinates are built on network connectivity graph, then network topology is utilized, but the coordinate size and routing table entries become large
Solution Approach 1:
The patent projects the network topology from its original high-dimensional graph structure into a lower-dimensional Euclidean space. This dimensional transformation maintains topological relationships necessary for adaptive routing while reducing the size of routing tables to polylogarithmic dimensions.
Data Source
AI summary
A method and apparatus is disclosed herein for scalable routing with greedy embedding. In one embodiment, the method comprises storing log(n) coordinates in a routing table, where n is the number of nodes in a network, and further wherein the log(n) coordinates are generated by constructing a greedy embedding that embeds a graph topology depicting connections between n nodes of a network into a geometric space so as to use greedy forwarding by generating a spanning tree out of a connection graph representing the connections between the n nodes of the network, decomposing the tree into at most n branches, assigning a set of geometric coordinates to vertices in the tree in an n-dimensional space, and projecting the set of geometric coordinates onto a k-dimensional space, where k is less than n, to create the log(n) coordinates; and routing packets via nodes of the network using the log(n) coordinates in the routing table.