Deterministic Triangle Detection in Graph Databases
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Solution Overview
Problem
Existing methods for detecting triangular topological structures in networks or databases face high computational loads and inefficiencies, particularly due to reliance on hash tables which can lead to collisions and non-deterministic runtime, making it difficult to find and track triangle relationships in large graphs.
Innovation Solution
A method and system that topologically models a network or database as a graph, using a neighborhood generator to create datasets, a reduction unit to trim neighborhoods, and a triangle neighbor detection unit to pairwise compare reduced datasets for common neighbors, thereby efficiently detecting triangle neighborhoods without the drawbacks of hash tables.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If hash tables are used to detect triangle relationships, then processing time is reduced to optimal expected time, but collisions occur causing performance degradation to linear-time access
Solution Approach 1:
The patent creates a copy of the adjacency matrix (called adj_copy) where rows and columns are permuted based on degree ordering. This copied structure allows triangle detection without actual hash table collisions, maintaining deterministic O(1) access while avoiding the reliability issues of hash tables.
Solution Approach 2:
The patent changes the parameter of data organization from hash tables to degree-ordered adjacency matrices. By sorting vertices by degree and reorganizing the adjacency structure accordingly, the system achieves consistent performance without the collision problems inherent in hash tables.
2Speed
If hash tables are used for triangle detection, then lookup time is optimized, but non-deterministic runtime is introduced due to collisions
Solution Approach 1:
The patent performs preliminary sorting of vertices by degree before triangle detection. This pre-ordering allows the adjacency matrix to be structured such that triangle detection always follows a consistent pattern, eliminating non-deterministic runtime while maintaining fast lookup speeds.
3Quantity of substance
If hash tables are used to store neighborhood data, then space complexity is reduced to linear space, but rebuilding is required when graph changes occur
Solution Approach 1:
The degree-ordered adjacency matrix structure is self-updating. When the graph changes, vertices naturally maintain their degree-based ordering without requiring complete rebuilding of the data structure. The matrix automatically reflects current graph topology through its inherent ordering property.
4Reliability
If perfect hash tables are used to mitigate collisions, then constant-time access is maintained in worst-case, but randomization is required and parallel computation becomes difficult
Solution Approach 1:
The patent segments the adjacency matrix into degree-ordered sections, creating a structured approach that avoids the need for randomization. Each vertex neighborhood is processed in a systematic manner based on degree ordering, enabling deterministic performance without the complexity of perfect hash tables or randomization.
Data Source
AI summary
A method and system are provided for non-redundant detection of coactively linked nodes/data elements of a network or database topologically disposed in at least one triangularly linked arrangement. The network/database is topologically modelled as a graph having a plurality of vertices connected by edges. A neighborhood is generated in computer readable form for each connected vertex containing all other vertices directly connected thereto as neighbors. Connected vertex are ordered according to degree based on the number of neighbors. A reduced neighborhood is formed for each connected vertex by adaptively removing any lower order neighbor. Triangle neighborhoods are generated responsive to forward detections of common triangle neighbors through pairwise comparisons of reduced neighborhoods for connected vertices and each of their higher order neighbors, and reverse detection for certain connected vertices as triangle neighbors by lower ordered neighbors. Linked nodes/data elements are thereby screened in computationally mitigated manner to reveal coactive groupings.