Deferred Edge-Weight Graph Traversal for Computational Efficiency
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Solution Overview
Problem
Current graph traversal methods are impractical for certain problem domains due to high computational overheads and complexities, especially in edge-weight computations and complete graph construction.
Innovation Solution
The proposed method defers edge-weight computations, avoids redundant calculations, and constructs incomplete graphs during path determination, allowing for optimal, locally optimal, and near-optimal path identification without initial complete graph construction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If complete graph construction is performed before traversal, then optimal path determination can be achieved, but computational overhead and complexity increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing edge weight metrics during graph construction, so that during traversal operations, these pre-computed values can be directly used without recalculating complex edge weights, thus reducing computational overhead while maintaining optimal path determination
Solution Approach 2:
The patent implements dynamics by allowing the graph structure to be dynamically adjusted during traversal - edges can be added or removed based on traversal progress, and the graph can be reweighted using pre-computed metrics, enabling flexible optimization without reconstructing the entire graph
2Measurement precision
If edge-weight computations are performed completely before traversal, then accurate path costs are obtained, but computational time and resources are wasted on redundant calculations
Solution Approach 1:
The patent applies partial action by computing edge weights only when necessary during traversal rather than computing all edge weights completely beforehand. The pre-computed metrics provide sufficient information for accurate path cost determination without requiring full edge-weight computation for every possible edge
Solution Approach 2:
The patent changes parameters by using pre-computed edge weight metrics as substitutes for complete edge-weight computations. These metrics capture the essential cost information needed for optimal path determination while requiring significantly less computational effort than full edge-weight calculations
3Productivity
If incomplete graphs are used during traversal, then computational burden is reduced, but graph construction complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the graph into manageable components - using pre-computed edge weight metrics as separate reusable units that can be combined during traversal. This allows the graph to be processed in segments rather than as a monolithic structure, improving traversal efficiency while managing construction complexity
Data Source
AI summary
The current application is directed to optimal, locally optimal, and/or near-optimal path determination that defers edge-weight computations, avoids redundant edge-weight computations, and that does not require initial complete graph construction. Many real-world problems are not efficiently solved by current graph-traversal-determination methods because of the overheads and computational complexities involved in edge-weight computations. Moreover, it may be difficult or impossible to construct complete graphs to which current graph-traversal-determination methods can be applied. The currently disclosed optimal, locally optimal, and/or near-optimal path-determination methods and systems construct incomplete graphs during optimal, locally optimal, and/or near-optimal path determination, deferring node generation and edge-weight computations until necessary to expand incomplete graphs during the search for optimal, locally optimal, and/or near-optimal graph-traversal paths.