Data Coreset Compression With Logarithmic Size and Error Bounds
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Solution Overview
Problem
Existing data compression techniques for large-scale sensor networks, such as the Douglas-Peucker heuristic, face challenges with unbounded output size, high computational complexity, and linear growth in storage requirements, making them inefficient for handling and merging large datasets.
Innovation Solution
A method that compresses data by selecting a coreset of points using a procedure that limits the number of line segments to grow logarithmically with the number of points, ensuring a guaranteed level of accuracy and reducing computational and storage requirements, while allowing for parallel processing and efficient error bounds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the Douglas-Peucker heuristic is used for data compression, then the compression algorithm is simple and easy to implement, but the output size becomes unbounded and grows linearly with input size
Solution Approach 1:
The patent changes the fundamental parameter controlling output size from an unbounded greedy selection to a bounded logarithmic structure. By organizing points into hierarchical levels where each level contains at most one point per input interval, the output size is mathematically constrained to grow as O(log n) rather than linearly with input size n, while preserving the simplicity of the heuristic approach.
Solution Approach 2:
The patent segments the compressed data into hierarchical levels, where each level represents a different scale of approximation. This segmentation allows the system to control the number of points at each level independently, ensuring that the total output size remains bounded by the logarithm of the input size while maintaining implementation simplicity through modular processing.
2Ease of manufacture
If the Douglas-Peucker heuristic is used for data compression, then the algorithm is easy to implement, but the computational complexity becomes high
Solution Approach 1:
The patent changes the computational parameter from processing all n input points with O(n²) complexity to processing only O(log n) output points with O(log² n) complexity. This parameter change transforms the computational burden from quadratic to logarithmic squared, dramatically improving efficiency while keeping the algorithm simple through the same level-based construction approach.
3Quantity of substance
If a larger error threshold ε is chosen in Douglas-Peucker, then the compressed set size may be reduced, but the set may become too small or empty for effective compression
Solution Approach 1:
The patent introduces dynamic adaptability through its level-based structure, where the effective error threshold varies automatically across different levels of the hierarchy. Lower levels provide fine-grained approximation with smaller effective ε, while higher levels provide coarse approximation with larger effective ε, allowing the system to maintain both small output size and high compression quality without manual tuning.
Solution Approach 2:
By segmenting the compression into hierarchical levels, the patent allows different error thresholds to apply at different levels. This segmentation resolves the contradiction by enabling the system to use larger effective error thresholds at higher levels (reducing point count) while maintaining smaller effective error thresholds at lower levels (preserving quality), thus achieving both small compressed size and high precision.
4Reliability
If merged sets from streaming compression are used, then the error bound is preserved, but the set size increases linearly with the input stream
Solution Approach 1:
The patent employs merging of hierarchical structures from multiple input streams or segments. When merging two compressed datasets, the system combines their level-based representations and reconstructs the hierarchical structure, ensuring that the error bound is preserved while the output size grows only logarithmically with the combined input size rather than linearly.
Solution Approach 2:
The patent changes the scaling parameter for merged outputs by resetting the level indexing after merging. This parameter change ensures that the merged result maintains the logarithmic size property relative to the total input size, preventing linear growth while preserving the error bound through proper reconstruction of the hierarchical structure from the merged components.
Data Source
AI summary
An approach to compression of a large (n point or samples) data set has a combination of one or more desirable technical properties: for a desired level of accuracy (ε), the number of compressed points (a “coreset”) representing the original data is O(log n); the level of accuracy comprises a guaranteed bound expressed as multiple of error of an associated line simplification of the data set; for a desired level of accuracy and a complexity (e.g., number k of optimal line segments) of the associated line simplification, the computation time is O(n); and for a desired level of accuracy (c) and a complexity of the associated line simplification, the storage required for the computation is O(log n).