Subset Sum Matching Search Approach for Combinatorial Optimization
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Solution Overview
Problem
Existing methods for finding subsets of matching sums of items associated with two parties are inefficient and costly due to their exponential time complexity, making them intractable for large datasets.
Innovation Solution
A method implemented by a processor that receives two sets of data items, divides the larger set into two subsets, generates subset sums for each subset using a list and a hash-map, and detects matches between the subset sums based on a selected matching threshold.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a brute-force approach is used to explore all possible combinations of items from two parties, then all potential matches can be found, but the time cost grows exponentially and becomes intractable as the number of items increases
Solution Approach 1:
The patent divides the second set of data items into two subsets, generating subset sums for each subset separately. This segmentation reduces the problem size from exploring all combinations of two full sets to exploring combinations of smaller subsets, thereby reducing exponential time complexity while maintaining completeness of match detection.
Solution Approach 2:
The patent transforms the combinatorial search problem into a different dimensional space by generating subset sums and storing them in a hash-map. Instead of directly comparing all possible combinations of items, the solution creates a new representation (subset sums) that enables efficient matching through hash-based lookup, changing the problem from combinatorial enumeration to algebraic transformation and search.
2Adaptability or versatility
If the number of data items in the second set increases to provide more matching options, then the ability to find matches improves, but the computational complexity increases exponentially
Solution Approach 1:
By dividing the larger set into two subsets, the patent enables the system to handle larger numbers of data items without exponential complexity growth. The segmentation allows independent processing of smaller subsets and efficient combination of results, maintaining adaptability while controlling computational complexity.
Solution Approach 2:
The patent changes the parameter representation from individual items to subset sums. This transformation allows the system to work with aggregated values that capture the essential matching information while reducing the search space. The hash-map stores subset sums as keys, enabling efficient retrieval and comparison without enumerating all original item combinations.
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 a second set of data items; dividing the second set of data items into a first subset and a second subset; generating, based on the first subset, a first set of subset sums, and storing the first set of subset sums as a list; generating, based on the second subset, a second set of subset sums, and storing the second set of subset sums as a hash-map in conjunction with a corresponding hash function; and detecting, based on the first set of data items, the list, and the hash-map, at least one match between a subset sum that corresponds to the second set of data items and a subset sum that corresponds to the first set of data items.