Algorithm Data Transfer Rate Quantification via Laplacian Matrix
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Solution Overview
Problem
Existing methods for quantifying algorithmic data transfer rates are not intrinsic to the algorithms themselves, being influenced by target platforms and lacking support for multigrain data transfer analysis, making them platform-dependent and incomplete.
Innovation Solution
A method using algebraic theory, specifically dataflow graphs and matrices like Laplacian and incidence dependency matrices, to quantify intrinsic data transfer rates at various granularities, enabling platform-independent measurements that are unbiased towards hardware or software implementations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing techniques (software instrumentation or platform profiling) are used to measure data transfer rates, then computational complexity can be extracted, but the measurements are biased by target platforms and not intrinsic to algorithms themselves
Solution Approach 1:
The patent extracts the data transfer rate measurement from the platform-dependent context and formulates it as an intrinsic algorithmic property. By using dataflow graphs and spectral graph theory, the method separates the algorithmic complexity from hardware/software implementation details, allowing measurement without platform bias.
Solution Approach 2:
The patent introduces dataflow graphs and spectral graph theory as intermediary mathematical models to bridge the gap between algorithmic complexity and data transfer requirements. These intermediaries enable platform-independent analysis by translating algorithmic operations into graph-theoretic formulations that capture intrinsic properties.
2Device complexity
If data transfer rates are measured at a single data granularity, then measurement is simplified, but multigrain analysis capability is lost
Solution Approach 1:
The patent segments the dataflow graph into multiple granularity levels, allowing analysis at different scales. By partitioning the graph based on data reuse patterns and using spectral clustering, the method enables simultaneous measurement at fine-grain and coarse-grain levels without requiring separate measurement systems.
Data Source
AI summary
The quantifying method for intrinsic data transfer rate of algorithms is provided. The provided quantifying method for an intrinsic data transfer rate includes steps of: detecting whether or not a datum is used; providing a dataflow graph G including n vertices and m edges, and a Laplacian matrix L having ixj elements L(i,j) when the datum is not reused, wherein each of the vertices represents one of an operation and a datum, each of the edges represents a data transfer, and vi is the ith vertex; and using the Laplacian matrix L to estimate a maximum quantity of the intrinsic data transfer rate.