Multi-Factor Evaluation Scheduling Algorithm
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
In computing systems, particularly in secure communication and cloud computing environments, multi-factor evaluations require optimizing the order of testing factors to minimize overall cost, which existing methods address inefficiently using burdensome exponential algorithms.
Innovation Solution
A method determines an optimal schedule for evaluating multiple factors by sorting them based on a precedence relation that minimizes the overall cost expectation, employing a sub-quadratic algorithm and enabling parallelization, specifically using a variant of the Quicksort sorting algorithm to reduce comparisons from n! to O(n ln n.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a straightforward approach is used to minimize the mathematical expectation of evaluation cost, then the optimal order can be determined, but the algorithm becomes exponentially complex and burdensome
Solution Approach 1:
The patent transforms the optimization problem from minimizing expected cost directly to sorting factors based on a derived parameter (cost multiplied by success probability). This parameter transformation converts an exponentially complex optimization search into a polynomial-time sorting operation, resolving the contradiction between optimality and algorithmic complexity.
Solution Approach 2:
Instead of searching through all possible permutations to find the optimal order, the patent inverts the approach by deriving a sorting criterion that directly yields the optimal sequence. This inversion transforms the problem from exhaustive search to efficient sorting, eliminating exponential complexity while preserving optimality.
2Reliability
If multiple factors are evaluated to ensure security, then authentication reliability improves, but the time and computational resources required increase
Solution Approach 1:
The patent pre-calculates and stores the sorting criterion (cost × probability) for each factor before authentication. During actual authentication, factors are simply evaluated in the pre-determined optimal order, eliminating the need for real-time optimization calculations and reducing evaluation time while maintaining security.
Solution Approach 2:
The patent replaces the mechanical process of trial-and-error or exhaustive search for optimal ordering with a mathematical sorting mechanism. This substitution transforms the evaluation system from one requiring complex real-time computation to one using simple comparative sorting, significantly reducing computational overhead and time loss.
3Measurement precision
If all factors are evaluated completely, then measurement precision is maximized, but the computational cost increases exponentially
Solution Approach 1:
The patent changes the computational parameter from evaluating all permutations (n!) to evaluating sorted pairs of factors (O(n ln n)). This parameter transformation maintains the precision of determining the optimal sequence while dramatically reducing the computational energy required, as sorting is exponentially more efficient than exhaustive permutation evaluation.
Data Source
AI summary
Techniques are disclosed for optimally scheduling computations that involve multiple factors, the cost of evaluations and probabilities of success of which are known. For example, a methodology is provided for determining an optimal schedule of a multi-factor test in sub-quadratic time. While the methodology has wide ranging application, we illustrate a particular applicability to a security application involving multi-factor authentication in a cloud computing environment, as well as applicability to the contact center agent scheduling.