Accelerating the General Simplex Procedure for Linear Real Arithmetic via GPUs

  • Steven T. Stewart
  • Derek Rayside
  • Vijay Ganesh
  • Krzysztof Czarnecki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9971)


This paper demonstrates the benefits of GPU parallelism for a simplex-based decision procedure for conjunctions of linear constraints over reals. This variant of the simplex method, called general simplex, decides whether the set of constraints is satisfiable, and is intended to be integrated into SMT solvers. We carried out comprehensive experiments over randomly generated instances for dense linear programming problems on a mid-range consumer GPU (AMD Radeon 390X) using floating point arithmetic. The GPU scheduled hundreds of thousands of concurrent thread workgroups to process tableaus representing up to 8k variables and 8k constraints. We achieved speedup up to 25x over a CPU-only implementation (quad-core AMD Kaveri 3.7 GHz) of the same procedure. We compared this to a multithreaded OpenMP implementation that also achieved up to 1.8x speedup on the same inputs. These results suggest that GPU processors may be further utilized in the context of SMT and software verification tools.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Steven T. Stewart
    • 1
  • Derek Rayside
    • 1
  • Vijay Ganesh
    • 1
  • Krzysztof Czarnecki
    • 1
  1. 1.University of WaterlooWaterlooCanada

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