Optical Path Computation Using Reachability Matrix Multiplication
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Solution Overview
Problem
Optical path computation in optical networks often requires determining end-to-end reachable paths with a minimum number of regenerators, which is complex and costly, especially when direct reachability is absent between source and destination nodes, necessitating the use of electrical regeneration.
Innovation Solution
The method involves generating a reachability matrix representing nodes and direct directional paths, using matrix multiplication to determine the number of regenerators needed for reachability, and successively multiplying the resultant matrix until a specific value is achieved, thereby identifying regenerators and possible paths without relying on graph transformation algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If graph transformation algorithms are used to determine end-to-end reachable paths with minimum regenerators, then path computation accuracy is improved, but device complexity and engineering effort increase significantly
Solution Approach 1:
The patent replaces complex graph transformation algorithms with matrix multiplication operations. Specifically, it uses binary adjacency matrices to represent network topology and employs matrix multiplication to compute transitive closure, which identifies all reachable node pairs and the minimum number of regenerators required. This substitution of mathematical operations for algorithmic graph processing significantly reduces computational complexity while maintaining accuracy in determining end-to-end reachable paths.
Solution Approach 2:
The patent transforms the network topology representation from graph-based to matrix-based parameters. By encoding network connectivity as binary values in an adjacency matrix (1 for direct connectivity, 0 for no connectivity), the system enables efficient computation of reachable paths through successive matrix multiplications. This parameter transformation allows the computation of minimum regenerator counts by analyzing the powers of the adjacency matrix, where A^k reveals paths of length k.
2Reliability
If electrical regenerators are used when direct reachability is absent, then end-to-end path connectivity is achieved, but network cost and resource consumption increase
Solution Approach 1:
The patent performs preliminary computation of the transitive closure of the network topology using matrix multiplication before actual path establishment. By pre-calculating all reachable node pairs and the minimum number of regenerators required for each pair, the system can make informed decisions about when electrical regeneration is necessary. This preliminary analysis enables optimization of regenerator placement and selection of paths that minimize the number of regenerators, thereby reducing network cost and energy consumption while ensuring connectivity.
Data Source
AI summary
Methods and systems for optical path computation based on a reachability matrix may rely on matrix multiplication to determine a number and respective network locations of regenerators for establishing an end-to-end reachable path in an optical network between a source node and a destination node. The reachability matrix may specify directly reachable optical paths between nodes in the optical network.