Subset Sum Matching via Dynamic Programming Tables
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing combinatorial optimization methods for finding subsets of matching sums across two parties are inefficient and costly due to exponential time complexity, particularly in tasks like reconciliation of financial records, which are labor-intensive and prone to fraudulent detection.
Innovation Solution
A method involving data discretization, reorganization into positive integer groups, and binary tree search is employed to identify subset sum matches, using threshold-based validation and vector concatenation to optimize the process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If brute-force approach is used to explore all possible combinations, then completeness of subset sum matching is ensured, but computational time grows exponentially and becomes intractable
Solution Approach 1:
The patent segments the problem by dividing the two sets of data items into positive and negative groups separately, then processes each group independently through dynamic programming tables. This segmentation reduces the search space complexity while maintaining completeness of matching identification.
Solution Approach 2:
The patent performs preliminary discretization of data items and pre-computation of dynamic programming tables before the actual matching process. This preliminary action transforms the exponential-time brute-force search into a polynomial-time process by pre-establishing feasibility information in structured tables.
2Loss of time
If dynamic programming approach with discretization is used, then computational time is significantly reduced, but data precision may be affected by discretization process
Solution Approach 1:
The patent applies discretization as a parameter transformation technique, converting continuous or high-precision data into discrete representations that are suitable for dynamic programming. This parameter change enables efficient computation while maintaining sufficient precision for financial reconciliation tasks through controlled discretization levels.
3Measurement precision
If conventional reconciliation methods are used, then accuracy of financial record comparison is maintained, but labor intensity is high and fraudulent detection is prone
Solution Approach 1:
The patent replaces manual mechanical reconciliation processes with an automated computer-based dynamic programming system. The mechanical manual comparison of financial records is substituted by algorithmic processing that automatically identifies matching subsets, significantly reducing labor intensity while maintaining or improving accuracy through systematic exhaustive search within constrained search spaces.
Data Source
AI summary
Methods and systems for performing a combinatorial optimization task are provided. The method includes: receiving a first set of data items and discretizing each of the first set of data items in order to generate a first discretized set of data items; receiving a second set of data items and discretizing each of the second set of data items in order to generate a second discretized set of data items; reorganizing the first and second discretized sets of data items into two respective groups of positive integers; using the two groups of positive integers to generate two respective tables for storing a feasibility of obtaining at least one subset sum from among the elements of the first and second discretized sets of data items; and performing a subset sum matching procedure upon the two tables in order to identify the at least one subset sum.