The Subset Sum Matching Problem

2025-08-26

AI Summary

This paper introduces the Subset Sum Matching Problem (SSMP), a novel combinatorial optimization problem motivated by real-world financial transaction reconciliation. Due to its NP-hardness, we propose two polynomial-time approximation algorithms—one with a constant-factor approximation guarantee and another with a bounded relative error—and an exact branch-and-bound algorithm. We construct the first SSMP benchmark dataset, systematically varying instance scale, sparsity, and noise level. Comprehensive evaluation on this dataset shows that the exact algorithm guarantees optimal solution quality, while the approximation algorithms solve large-scale instances in milliseconds with average error below 3%. This work bridges a theoretical gap in modeling and solving financial reconciliation tasks via combinatorial optimization, providing a scalable, principled methodology for industrial deployment.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements

Abstract

This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one optimal, to solve this problem. We also generate a benchmark to cover different instances of SSMP varying in complexity, and carry out an experimental evaluation to assess the performance of the approaches.

Problem

• Introduces the Subset Sum Matching Problem for financial reconciliation
• Presents three algorithms including optimal and suboptimal solutions
• Evaluates performance through benchmark testing on varied instances

Innovation

• Developed three algorithms for SSMP
• Included optimal and suboptimal solution approaches
• Created benchmark for experimental performance evaluation