Graph Optimization Using Path Count Data Structures
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional graph optimization methods, such as calculating the average shortest path length, are computationally expensive and inefficient for large graphs, as they require considering all paths between all node pairs, leading to significant computational costs.
Innovation Solution
A method involving a data structure that stores the count of paths of varying lengths between node pairs, allowing for the estimation of objective functions indicative of node connections and system performance without the need for extensive calculations, by modifying the graph based on edge additions and subtractions and using temporary data structures to calculate changes in shortest path lengths.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional graph optimization methods calculate the objective function (average shortest path length) for all node pairs, then the optimization accuracy is improved, but the computational time becomes prohibitive for large graphs
Solution Approach 1:
The patent segments the graph into multiple partitions and processes each partition independently. Instead of calculating shortest paths for all node pairs in the entire graph, the method divides the computation into smaller sub-problems for each partition, significantly reducing the computational complexity and time required while maintaining optimization accuracy.
Solution Approach 2:
The patent pre-calculates and stores the number of shortest paths between node pairs in a data structure before optimization begins. This preliminary action allows the optimization algorithm to efficiently query path information during graph modifications without performing repeated full graph traversals, thereby reducing computation time while preserving measurement precision.
2Reliability
If the graph is modified to optimize connections between nodes, then the system performance is improved, but the computational burden increases due to re-evaluating all paths
Solution Approach 1:
The patent implements a dynamic optimization approach where the graph is modified incrementally and the objective function is updated efficiently after each modification. Instead of re-evaluating all paths from scratch, the method dynamically adjusts the path counts and objective function values based on local changes, maintaining system performance improvement while preserving computational efficiency.
Solution Approach 2:
The patent uses a data structure that stores copied path information between node pairs. When the graph is modified, the system updates this stored path information selectively rather than recalculating all paths, effectively using a copy of the path data to maintain performance metrics without the full computational burden of重新计算所有路径.
Data Source
AI summary
A method includes generating, using a processor, a graph including a plurality of nodes and a plurality of paths between the nodes, the graph representing a system comprising an arrangement of elements, and a data structure in which, for each node pair of the plurality of nodes, a count of the number of paths of length S between the node pair is stored in association with the length S. The method includes modifying the graph, using the processor, to obtain a modification of the graph related to the count of the number of paths of length S, and estimating, based on the data structure and the modification, an objective function that is quantitatively representative of the connections between the nodes and being indicative of performance of the system.