Memory-Efficient Optical Path Computation via Transitive Closure
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Solution Overview
Problem
Existing optical path computation methods in optical networks are inefficient due to high memory consumption during the computation of reachability matrices, which limits computational feasibility, especially in large networks with thousands of nodes.
Innovation Solution
A memory-efficient method for optical path computation using a single matrix M that represents the minimum number of all-optical paths between nodes, calculated through an iterative in-place transitive closure algorithm, reducing memory consumption and enabling efficient computation of reachability matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional reachability matrix computation methods are used, then complete optical path information can be obtained, but memory consumption becomes excessively high
Solution Approach 1:
The patent segments the computation process into iterative steps where the matrix M is updated progressively. Instead of computing and storing all reachability matrices simultaneously, the method divides the transitive closure computation into N-1 iterations, where each iteration refines the matrix M by incorporating paths through node k. This segmentation allows the computation to proceed with minimal memory footprint while still achieving complete optical path information.
Solution Approach 2:
The patent merges the information from multiple reachability matrices into a single matrix M that stores the minimum number of all-optical paths between node pairs. By combining the reachability information from iterations k=1 to N-1 into one consolidated matrix, the method eliminates the need to store separate matrices for each iteration, thereby reducing memory consumption while preserving complete path computation capability.
2Reliability
If multiple reachability matrices are computed and stored, then comprehensive path information is available, but computational complexity increases
Solution Approach 1:
The patent performs preliminary action by initializing matrix M with direct link information before the iterative transitive closure computation. The initial matrix M is populated with the number of all-optical paths between directly connected nodes, establishing a foundation that eliminates the need to recompute basic connectivity during iterations. This preliminary setup reduces the computational burden during the main computation phases.
Solution Approach 2:
The patent uses copying by maintaining a working copy of matrix M that is updated iteratively. Instead of managing multiple separate reachability matrices, the method creates a single working copy that is refined through N-1 iterations of transitive closure. Each iteration copies and updates the matrix M in-place, eliminating the need to store and process multiple full matrix copies simultaneously, thereby reducing computational complexity.
3Measurement precision
If exact minimum path computation is performed, then optimal regenerator placement is achieved, but computation time increases
Solution Approach 1:
The patent changes the parameter being computed from binary reachability (yes/no) to quantitative path counting (minimum number of paths). By modifying matrix M to store the actual count of all-optical paths rather than simple reachability indicators, the method enables direct determination of optimal regenerator placement through threshold comparisons. This parameter change allows exact computation of minimum paths while using efficient matrix operations that maintain reasonable computation time.
Solution Approach 2:
The patent maintains continuity of useful action by performing in-place updates of matrix M throughout the N-1 iterations. Each iteration continuously refines the path count information without discarding previous results, allowing the computation to build upon prior work. This continuous refinement approach ensures that by the final iteration, the matrix contains exact minimum path information while avoiding redundant computations that would increase overall computation time.
Data Source
AI summary
A matrix M indicating a minimum number of all optical paths between pairs of nodes may be generated in one embodiment using an algorithm for transitive closure. In various embodiments, different algorithms and methods may be used to generate matrix M. Once a convergent matrix M has been generated that attains transitive closure, any corresponding reachability matrix RM^a may be obtained from matrix M in a computationally efficient manner. Matrix M may be used to determine groups of potential regenerator placements and obtain end-to-end optical paths by selecting desired sequences of regenerators.