Network Path Computation with Virtual Vertex and Segmentation
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Solution Overview
Problem
Current path computation methods in networks face challenges with unordered inclusion and regional revisit constraints, particularly due to the NP-completeness of unordered constraints and the computational hardness of regional revisit constraints, leading to inefficient scaling and high time and space complexity.
Innovation Solution
The method employs an efficient mapping of the Traveling Salesperson (TSP) heuristic to provide a bounded approximation for unordered inclusion constraints and incorporates a strategy to shorten the k-shortest path search by adding a virtual vertex and removing edges to avoid regional revisit, allowing for efficient path computation in networks with symmetric weight assumptions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all permutations within an unordered inclusion set are attempted to find the exact shortest path, then the solution accuracy is improved, but the computational complexity increases exponentially (NP-complete)
Solution Approach 1:
The path computation is segmented into multiple shortest path problems, one for each segment between consecutive inclusion nodes. Instead of solving one complex NP-complete problem considering all permutations, the algorithm divides it into N+1 polynomial-time shortest path problems (using Dijkstra's algorithm), where N is the number of inclusion nodes. This segmentation transforms the exponential complexity into polynomial complexity while maintaining solution accuracy.
Solution Approach 2:
The algorithm performs preliminary actions by pre-computing and storing the shortest path distances between all pairs of inclusion nodes before solving the unordered inclusion problem. This preliminary computation enables the subsequent dynamic programming approach to efficiently combine these pre-computed segments without re-computing paths, significantly reducing the overall computational burden.
2Reliability
If k-shortest path enumeration is used to filter paths satisfying regional revisit constraints, then the constraint satisfaction is improved, but the time and space complexity increases significantly
Solution Approach 1:
The algorithm extracts and removes inclusion nodes from the graph after computing the shortest path to each node, preventing revisits to already-visited nodes. This extraction approach naturally enforces the regional revisit constraint without requiring expensive k-shortest path enumeration and post-processing filtering, thereby maintaining constraint satisfaction while improving computational efficiency.
Solution Approach 2:
The patent introduces a virtual node that acts as an intermediary to handle the unordered inclusion constraints. This virtual node connects to all inclusion nodes and enables the algorithm to compute paths that visit all inclusion nodes without specifying the order, while the dynamic programming approach ensures regional revisit constraints are satisfied. This intermediary structure avoids the need for exhaustive k-shortest path enumeration.
3Productivity
If conventional approaches with ad-hoc cut-off or space bounds on k-shortest enumeration are used, then the computational resources are reduced, but the approximation quality and worst-case bounds become uncontrolled
Solution Approach 1:
The algorithm employs dynamic programming with a state space that dynamically tracks the set of visited inclusion nodes. The DP state transitions are governed by polynomial-time shortest path computations, providing controlled and predictable resource usage. This dynamic approach ensures both polynomial-time complexity and bounded approximation quality, avoiding the uncontrolled behavior of ad-hoc cut-off methods.
Data Source
AI summary
Systems and methods include receiving a request for a path from a source node to a destination node in a network with the request including N unordered inclusion nodes, N≥1; adding a virtual vertex in a graph with edges connected to each of the N inclusion nodes, wherein the graph includes the virtual vertex, vertices representing nodes in the network, and edges representing links; determining a shortest path from the source node to the virtual vertex and removing an edge from a first inclusion node, that is on the shortest path, from the virtual vertex; if N>1, determining a shortest path N times to find path segments between the N inclusion nodes, removing an edge from each of the N inclusion nodes from the virtual vertex when on a corresponding shortest path; and determining a shortest path from a last inclusion node to the destination node.