Bit-Vector Graph Connectivity Metrics for Large Networks
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Solution Overview
Problem
Existing graph analysis algorithms are inefficient for determining connectivity-metrics in large graphs, particularly due to high computational expense and potential for stack overflow errors, making real-time analysis infeasible.
Innovation Solution
The use of bit-vector algorithms that generate logical bit-vectors representing connectedness between nodes or edges, allowing for efficient determination of connectivity-metrics through iterative logical operations, reducing computational time and memory requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If unrestricted recursive functions are used to determine connected components, then the algorithm runs quickly, but it may cause stack overflow if the graph is too large
Solution Approach 1:
The patent segments the graph traversal problem into smaller manageable units by using iterative approaches with explicit stack data structures, dividing the computation into manageable chunks that can be processed without overwhelming system resources
Solution Approach 2:
The patent introduces intermediary data structures (such as work queues and distance arrays) that mediate between the input graph and the output connectivity metrics, allowing the algorithm to process large graphs without direct recursive calls that could cause stack overflow
2Reliability
If restricted recursive depth is used to avoid stack overflow, then the algorithm is safer, but it is considerably slower and may fail if the recursive depth allowed is shorter than the graph's diameter
Solution Approach 1:
The patent employs dynamic data structures and adaptive processing that adjust to the graph's characteristics, using iterative deepening or dynamic programming approaches that can handle graphs of any diameter without being constrained by fixed recursive depth limits
Solution Approach 2:
The patent transforms the problem from a depth-first recursive search (one-dimensional in terms of call stack depth) to a breadth-first or iterative approach using heap-allocated data structures, effectively adding another dimension of memory management that eliminates stack overflow constraints
3Reliability
If conventional algorithms are used for determining connectivity-metrics in large graphs, then the algorithms are well-established, but the processing required is very expensive making real-time analysis infeasible
Solution Approach 1:
The patent performs preliminary actions by pre-computing and storing connectivity information in optimized data structures (such as adjacency lists and distance arrays), allowing subsequent queries to be answered rapidly without re-computing entire connectivity metrics
Solution Approach 2:
The patent changes the parameters of the computation by using bit-vector representations and parallel processing techniques, transforming the problem from sequential expensive computations to parallel efficient operations that maintain correctness while dramatically reducing execution time
Data Source
AI summary
Determination of a connectivity-metrics for graphs representative of networks of interest. A graph that represents a network of interest is accessed. The graph includes nodes representing points in the network of interest, and edges corresponding to the nodes. Bit-vectors are generated corresponding to the nodes and/or edges, wherein individual bits in the bit-vectors respectively provide a logical indication of connectedness. The connectivity-metric is then determined by applying a logical bit operation to the plurality of bit-vectors. Examples of connectivity metrics include a connected components, shortest paths, betweenness, clustering, and tree-based determinations.