A GPU accelerated variant of Schroeppel-Shamir’s algorithm for solving the market split problem
accepted for publication
- The market split problem (MSP), introduced by Cornu´ejols and Dawande (1998), is a challenging binary optimization problem on which state-of-the-art linear programming-based branch-and-cut solvers perform poorly. We present a novel algorithm for solving the feasibility version of this problem, derived from Schroeppel–Shamir’s algorithm for the one-dimensional subset sum problem. Our approach is based on exhaustively enumerating one-dimensional solutions of MSP and utilizing GPUs to evaluate candidate solutions across the entire problem. The resulting hybrid CPU-GPU implementation significantly outperforms a parallel CPU-only variant, efficiently solving instances with up to 10 constraints and 90 variables. We demonstrate the algorithm’s performance on benchmark problems, solving instances of size (9, 80) in less than fifteen minutes and (10, 90) in up to one day. Given our results, sorting based algorithms can be considered competitive for solving the MSP on modern hardware.
| Author: | Nils-Christian KempkeORCiD, Thorsten KochORCiD |
|---|---|
| Document Type: | In Proceedings |
| Parent Title (English): | Operations Research Proceedings 2025 |
| MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING |
| Year of first publication: | 2026 |
| ArXiv Id: | http://arxiv.org/abs/2507.05045 |
| Preprint: | urn:nbn:de:0297-zib-100554 |

